Financial Management

Chapter 3 CP - 10 The solution found using The Management Scientist is shown below. Objective Function Value = 61375.000 Variable Value Reduced Costs -------------- --------------- ------------------ R 17500.000 0.000 D 10624.999 0.000 H 5000.000 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 8.500 2 250.000 0.000 3 250.000 0.000 4 875.000 0.000 5 0.000 1.500 6 7500.000 0.000 7 7624.999 0.000 8 0.000 -0.175 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- R 1.500 1.650 2.000 D 1.892 2.000 2.200 H No Lower Limit 2.250 2.425 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 5390.000 6000.000 6583.333 2 7250.000 7500.000 No Upper Limit 3 7250.000 7500.000 No Upper Limit 4 5125.000 6000.000 No Upper Limit 5 6750.000 7500.000 7750.000 6 No Lower Limit 10000.000 17500.000 7 No Lower Limit 3000.000 10624.999 8 -0.000 5000.000 9692.307 3. From the dual prices it can be seen that additional almonds are worth $8.50 per pound to TJ. Additional walnuts are worth $1.50 per pound. From the slack variables, we see that additional Brazil nut, Filberts, and Pecans are of no value since they are already in excess supply. 4. Yes, purchase the almonds. The dual price shows that each pound is worth $8.50; the dual price is applicable for increases up to 583.33 pounds. Solutions to Case Problems CP - 11 Resolving the problem by changing the right-hand side of constraint 1 from 6000 to 7000 yields the following optimal solution. The optimal solution has increased in value by $4958.34. Note that only 583.33 pounds of the additional almonds were used, but that the increase in profit contribution more than justifies the $1000 cost of the shipment. Objective Function Value = 66333.336 Variable Value Reduced Costs -------------- --------------- ------------------ R 11666.667 0.000 D 17916.668 0.000 H 5000.000 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 416.667 0.000 2 250.000 0.000 3 250.000 0.000 4 0.000 5.667 5 0.000 4.333 6 1666.667 0.000 7 14916.667 0.000 8 0.000 -0.033 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- R 1.000 1.650 1.750 D 1.976 2.000 3.300 H No Lower Limit 2.250 2.283 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 6583.333 7000.000 No Upper Limit 2 7250.000 7500.000 No Upper Limit 3 7250.000 7500.000 No Upper Limit 4 4210.000 6000.000 6250.000 5 7250.000 7500.000 7750.000 6 No Lower Limit 10000.000 11666.667 7 No Lower Limit 3000.000 17916.668 8 0.002 5000.000 15529.412 5. From the dual prices it is clear that there is no advantage to not satisfying the orders for the Regular and Deluxe mixes. However, it would be advantageous to negotiate a decrease in the Holiday mix requirement.

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