Intro to Applied Stats

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2018 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. If the price-supply equation for CD players is given by: p = 0.04 x s − 10 then we can say that: "the supplier is willing to supply 10 CDs for free”. (5 marks) False , 250CDs 2. If the total revenue resulting from selling a certain product is given by the relation R =− 20 x 2 + 1200 x , then we can say that "Maximum revenue will occur when 100 units are sold ". (5 marks) False , 30 units 3. If the value of an office equipment is given by: V = 85000 ( 0.86 ) t where V is the value of the equipment in $ and t is the time in years since 2004 , then we can say that: “The value of the equipment is growing at a rate of 0.86 $ per year. (5 marks) False , decaying (decreasing) at a rate of 14 %/ year 1 October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2018 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) MSA produces plastic chairs. Total monthly fixed costs for the production of chairs are $8,000, while variable costs amount to $25 per chair and include packaging and distribution costs for each chair actually sold to a retailer. The chairs are sold to retail outlets at $45 each. a) Determine the linear revenue equation R = f ( x ) , where R is the total revenue in $ resulting from selling x chairs (2marks) R = px = 45 x b) Determine the linear cost equation C = f ( x ) , where C is the total costs in $, and x is the number of chairs produced. (3 marks) C = 8000 + 25 x c) Determine the linear profit equation P = f ( x ) . (2marks) P = R − C = 20 x − 8000 d) What is the profit/loss if the company sells300 chairs?( 5 marks) P = 20 ( 300 )− 8000 =− $ 2000 , Loss e) How many chairs should the company sell to break even? (3marks) To break even P= 0, 20 x − 8000 = 0 → x = 400 chairs 2 October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Spring 2018 Math for Economists I Model Answer MTH_113/ECO113 Problem 2: (15 marks) The market research department of MSA CO. predicts that the price-demand equation for its T-shirts is given by p =− 0.05 x + 10 , where p is the selling price in dollars and x is the number of T-shirts it can sell in one week. a) Determine the quadratic weekly revenue function R = f ( x ) . (4 marks) R = px =− 0.05 x 2 + 10 x b) How many T-shirts should be sold to achieve maximum revenue (4marks) x v =− b 2 a = − 10 − 0.1 = 100 T − shirts c) Determine the maximum revenue that could be achieved. (4 marks) R max =− 0.05 ( 100 ) 2 + 10 ( 100 )= 500 $ d) Determine the revenue if MSA sells 50 T-shirts. (3 marks) R =− 0.05 ( 50 ) 2 + 10 ( 50 )= 375 $ 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

MTH_113ModelAnswerMidTermFall2018.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 – 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

October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Fall 2019 Math for Economists I Model Answer MTH-113/ECO113 (Total Marks 100) S ECTION (I): (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. If the value of a refrigerator V in dollars as a function of time t in years since 2015 is given by the relation: then we can say that “the value of the refrigerator depreciates at a rate of 8000 refrigerator/month ” (5 marks) Fals e 400 $ /year 2. If the total cost of producing q units of a certain product is given by: then we can say that: "A minimum total cost of 1000$ will occur when 20 units are produced". (5 marks) Fals e 500 $ will occur when 50 units are produced 1. If the value of a cellular phone is given by: where V is the value of the phone 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 0.86 $ per year. (5 marks) Fals e decays at a rate of 14 % per month 1 8000 400    t V 1000 20 2 . 0 2    q q C t V ) 86 . 0 ( 800  October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Fall 2019 Math for Economists I Model Answer MTH-113/ECO113 S ECTION (II): P ROBLEM S OLVING : (85 marks) Part A:Answer only one of the following two problems (15 marks) Problem 1: (15 marks) Dina purchased a new car in 2012. The resale value (the market value) of the car (in dollars) was found to be $30,000 in 2015 and $24,000 in 2018. The relation between the market value of the car V (in dollars) and the time t in years since 2012 is assumed to be linear. a) Find the linear equation (8 marks). Linear equation (3, 30000) & (6, 24000) Slope b) What was the value of the car when Dina first purchased it in 2012? (3 marks). 36000$ c) Use the equation to estimate the value of the car (to the nearest $) in the year 2021 (4 marks). 1 ) ( t f V  b mt V   2000 3 6 30000 24000      m 000 , 36 2000 000 , 36 ) 3 ( 2000 30000        t V b b $ 18000 36000 ) 9 ( 2000     V October University for Modern Sciences & Arts (MSA) Faculty of Management Sciences Module Title: Math for Social Sciences II Final Exam – Fall 2019 Math for Economists I Model Answer MTH-113/ECO113 Problem 2: (15 marks) The market research department of MSA predicts that the price- demand equation for its University caps is given by: where p is the selling price per cap in dollars and q is the number of caps it can sell in one week. Meanwhile, the cost function for the above caps was found to be: Where C is the total weekly cost in dollars. a) Write an equation for the weekly revenue R as a function of price p. . (4 marks) b) Rewrite the cost equation as a function of price p. . (3 marks) c) Determine the quadratic weekly profit function . (5marks) d) At what price should each cap be sold to generate maximum weekly profit . (3 marks) 1 200 10    p q 160 4   q C ) ( p f R  p p pq R 200 10 2     ) ( p f C  960 40 160 ) 200 10 ( 4        p p C ) ( p f P  960 240 10 960 40 200 10 2 2            p p p p p C R P $ 12 20 240 2       a b p v

All courses in MATH

Popular Documents