Intro to Applied Stats

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2018 Model Answer Module Code: MTH113 Total Marks (100) S ECTION (I): T HEORETICAL S TUDY (Total:20 marks ) Answer the following questions (Q1) Define the following terms. (10 marks) 1. Domain of a Function y= f(x). (5 marks) It is the set of all possible values of x. 2. Marginal Cost. (5 marks) It is the additional cost resulting from producing one extra unit of a certain product. (Q2) Identify which of the following underlined statement is “True” and which is “False” and rewrite the exact underlined statement for the false ones. (10 marks) 1. If the profit function of a company which sells x units of a certain product is given by the relation: P = 15 x − 2000 , where P is in dollars, then we can say that the profit is “ decreasing at a rate of 2000 units ” (5 marks) False increasing at rate of 15 $ /unit 2. If the supply function of a certain product is given by the relation q s = 20 p 2 + 1200 , then we can say that “the supplier is willing to supply 30 units for free”. (5 marks) False 1200 units 1 October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2018 Model Answer Module Code: MTH113 S ECTION (II): P ROBLEM S OLVING (Total:80 marks ) Part A: Answer only one of the following two problems (40 marks) Problem 1 : (40 marks) The weekly demand for mouthwash in a chain of drug stores is 1160 bottles at a price of $3.79 each. If price is lowered to $3.59, the weekly demand increases to 1320 bottles. a) Find a price-demand equation of the form q d = mp + b , where p is the price per bottle in dollars and x is the corresponding weekly demand. (15 marks) (3.79, 1160) & (3.59, 1320) m = 1320 − 1160 3.59 − 3.79 =− 800 bottles /$ 1160 =− 800 ( 3.79 )+ b → b = 4192 q d =− 800 p + 4192 b) If the price-supply equation for the above product is given by: q s = 1000 p − 2000 , determine the market equilibrium price and quantity. (10 marks) For market equilibrium q s = q d 1000 p e − 2000 =− 800 p e + 4192 p e = 3.44 $ Substituting in the supply equation we get: q e = 1440 bottles c) If the stores charges $3.29 per bottle, determine the shortage or surplus of the number of bottles at that price. (15 marks) q d =− 800 ( 3.29 )+ 4192 = 1560 bottles 2 October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2018 Model Answer Module Code: MTH113 q s = 1000 ( 3.29 )− 2000 = 1290 bottles From the above, it is clear that we have a shortage of 270 bottles . Problem 2 : (40 marks) MSA purchased a new university bus in January 2012 for $18000 and estimated that it will have a value of $12000 after 6 years. If its value is depreciated linearly, a) Find a linear depreciation equation of the form V = mt + b that relates the value of the bus ( V ) in dollars to time ( t ) in years since January 2012. (15 marks) (0, 18000) & (6, 12000) m = 18000 − 12000 0 − 6 =− 1000 $/ year 18000 =− 1000 ( 0 )+ b → b = 18000 V = f ( t )=− 1000 t + 18000 b) Interpret the meaning of the slope of the depreciation line. (10 marks) Every year the value of the bus depreciates (decreases) by 1000 $ OR The value of the bus depreciates (decreases) at a rate of 1000 $/year OR As the time increases by one year, the value of the bus decreases by 1000$ c) What is the depreciated value of the bus in 2016? (5 marks) V = f ( 4 )=− 1000 ( 4 )+ 18000 = 14000 $ d) In what year will the value of the bus fall below $4,000? (10 marks) 3

MATH | 113 | Intro to Applied Stats | exam | October University for Modern 

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2019 Math for Economists I Model Answer MTH-113/ECO113 (Total Marks 100) S ECTION (I): T HEORETICAL PART (Total: 15marks ) Answer all questions Identify which of the following underlined statement is “True” and which is “False” and rewrite the exact underlined statement for the false ones. 1. I If the value of a computer V in dollars as a function of time t in years since 2010 is given by the relation: Then we can say that “the value of the computer depreciates at a rate of 4500 computer/month ” (5 marks) False depreciates at a rate of 300 $ / year 2. If the total revenue resulting from selling a certain product is given by the relation , where R is the total revenue in $ and x is the number of units sold, then we can say that " maximum revenue possible would be 250$ (5 marks) False 62500 $ 3. If the value of a cellular phone is given by: where V is the value of the equipment in $ and t is the time in months since the original purchase, then we can say that: “The value of the phone decays at a rate of 0.9 $ per year. (5 marks) False decays at a rate of 10 % per month 7 4500 300    t V x x R 500 2    t V ) 9 . 0 ( 5000  October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2019 Math for Economists I Model Answer MTH-113/ECO113 S ECTION (II): P ROBLEM S OLVING PART (Total: 85 marks ) Part A: Answer only one of the following two problems (15 marks) Problem 1: (15 marks) A demand curve for a commodity is the number of items the consumer will buy at different prices. It has been determined that at a price of $2 a store can sell 2400 plastic rulers, and at a price of $4 the store can sell 1200 such rulers. a) Assuming a linear relation, find a demand-price equation of the form: Where p is the price per ruler in $, and q d is the number of rulers sold per week. (8 marks) (2, 2400) & (4, 1200) Slope, m = (2400-1200)/ (2-4) = -600 Substitute (2, 2400) in the equation: 2400 = -600(2) + b; b = 3600 Therefore: b) If the supply-price equation for the above rulers is Determine the market equilibrium price and quantity. (7 marks) For market equilibrium Solving for p we get p e =4.8$ Substituting in either equation we get q e = 720 rulers 7 b mp p f q d    ) ( 3600 600 ) (     p p f q d 1200 400   p q s 3600 600 1200 400     p p October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2019 Math for Economists I Model Answer MTH-113/ECO113 Problem 2: (15 marks) A company started to produce a new brand of shampoo. The market research department predicts that the price-demand function for the new shampoo next month is controlled by the following function: Where p is the price of a single bottle (in dollars) and x is the number of bottles it can sell in one month. a) Write an equation for the Revenue as a function of p ; (7 marks) b) At what price should the company sell each bottle to maximize Revenue? (4 marks) c) Find the maximum Revenue possible. (4 marks) 7 50 5    x p ) ( p f R  p p x p R p x p x 10 2 . 0 . 10 2 . 0 50 5 2           $ 25 4 . 0 10 2       a b p v $ 125 ) 25 ( 10 ) 25 ( 2 . 0 2 max     R

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2019 Model Answer Module Code: MTH-113/ECO113 Total Marks (100) S ECTION (I): T HEORETICAL S TUDY (Total:20 marks ) Answer the following questions (Q1) Define the following terms. (10 marks) 1. Domain of a Function y= f(x). (5 marks) It is the set of all possible values of x . 2. Market Equilibrium. (5 marks) Market equilibrium exists if there is a price at which the quantity supplied equals the quantity demanded. Therefore market equilibrium occurs when (Q2) Identify which of the following underlined statement is “True” and which is “False” and rewrite the exact underlined statement for the false ones. (10 marks) 1. If the quantity supplied of a certain product is given by the following function: where q s is the quantity supplied in units and p is the selling price in dollars, then we can say that “ For every increase in the selling price by 3 $, the quantity supplied decreases by 100$ “.(5 marks) False increases by 60 units 2. I If the total Profit of producing and selling x units of a certain product is given by the relation: then 4 x x x d s   100 20   p q s 1000 1200 20 2     x x P October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2019 Model Answer Module Code: MTH-113/ECO113 we can say that "a maximum profit of 10000 units could be realized". (5 marks) False 17000$ S ECTION (II): P ROBLEM S OLVING (Total:80 marks ) Part A: Answer only one of the following two problems (40 marks) Problem 1 : (40 marks) The MSA Company started a new production line for its famous digital camera “the Nexus5”. Specifically, it was found that when the company produces 150 cameras per week, a total cost of 38400$ is incurred; when the production increase to 250 cameras per week, the total cost reaches 63400$. a) Use the above information to obtain a linear cost equation of the form: where C is the weekly total cost in dollars and x is the number of cameras produced per week. (15 marks) (150, 38400) & (250, 63400) Slope ( 150, 38400) b) From the above relation determine the marginal cost and interpret its meaning. (15 marks) Marginal cost = 250 $/camera 4 b mx C   camera m / $ 250 150 250 38400 63400     900 ) 150 ( 250 38400      b b 900 250   x C October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Spring 2019 Model Answer Module Code: MTH-113/ECO113 Interpretation : Every increase in the number of cameras produced by 1 camera, the total weekly cost increases by 250$. Or The total weekly cost increases at a rate of 250 $/camera c) What is the weekly fixed cost? (4 marks) Fixed cost = 900$ d) Determine the total weekly cost if the company produces 500 cameras. (6 marks) Problem 2 : (40 marks) Jasmine purchased a new car in January 2014. The market (book) value of the car was found to be 24000$ in January 2017 and 20000$ in January 2019. a) Use the above information to obtain a linear depreciation equation of the form which relates the value of the car V (measured in $) to the time t measured in years since January 2014. (20 marks) (3, 24000) & (5, 20000) Slope (3 , 24000) 4 $ 125900 900 ) 500 ( 250    C b mt t f V    ) ( year m / $ 2000 5 3 20000 24000      30000 ) 3 ( 2000 24000       b b 30000 2000 ) (     t t f V

MTH_113ModelAnswerFinalExamFall12019.docx.docx-October University for Modern Sciences &

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Fall 2018 Model Answer Module Code: MTH113/ECO113 Total Marks (100) S ECTION (I): T HEORETICAL S TUDY (Total:20 marks ) Answer the following questions (Q1) Define the following terms. (10 marks) 1. Total Revenue . (5 marks) It is the amount of money entering an organization from either selling products or providing services . 2. Marginal Revenue. (5 marks) It is the additional revenue resulting from selling one extra (more) unit of a given product (Q2) Identify which of the following underlined statement is “True” and which is “False” and rewrite the exact underlined statement for the false ones. (10 marks) 1. If the profit function of a company which sells x units of a certain product is given by the relation: , where P is in dollars, then we can say that “ 160 units have to be sold to break even ” (5 marks) True 2. I If the total Revenue resulting from selling a certain product is given by the relation: where p is the selling 2 2400 15   x P p p R 5000 100 2    October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Fall 2018 Model Answer Module Code: MTH113/ECO113 price in dollars, then we can say that "a maximum Revenue of 62500$ could be realized". (5 marks) True S ECTION (II): P ROBLEM S OLVING (Total:80 marks ) Part A: Answer only one of the following two problems (40 marks) Problem 1 : (40 marks) The demand for your college newspaper is 2000 copies each week if the paper is given away for free, and drops to 1000 copies each week if it is sold at a price of $2/copy. a) Find a price-demand equation of the form , where p is the selling price per copy in dollars and q d is the corresponding quantity of copies sold per week. (15 marks) (0, 2000) & (2, 1000) b) From the demand equation found in (a) above determine the slope of the line and interpret its meaning. (10 marks) Slope = -500 copies/$ Interpretation : Every increase in the price of the newspaper by 1 $, the quantity demanded (sold) decreases by 500 copies each week. Or 2 b mp q d   $ / 500 2 0 1000 2000 copies m      2000 ) 0 ( 800 2000      b b 2000 500    p q d October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Mathematics for Social Sciences II Mid Term Exam – Fall 2018 Model Answer Module Code: MTH113/ECO113 The number of weekly newspaper demanded (sold) decreases at a rate of 500 copies/$ c) If your college charges $2.5 per copy, how many copies will be sold at that price? (5 marks) d) At what price will no one buy the newspaper? (10 marks) Problem 2 : (40 marks) A company plans to market a new product. Based on its market studies, the company estimates that it can sell the new product for $20 per unit. Fixed costs are estimated to be $9000 to run the company while variable costs are estimated to be $10 for each unit produced. a) Find the revenue function R= f (x) , where R is the total revenue in $, and x is the number of units produced and sold. (5 marks) b) Find the cost function C= f (x), where C is the total costs in $, and x is the number of units produced. (5 marks) c) Find the profit function P=f (x) . (10 marks) 2 copies q d 750 2000 ) 5 . 2 ( 500     $ 4 2000 500 0     p p px R  x R 20  x C 10 9000  

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