B20 × ✓ fx A 1 Decision Variables 2 Products 12345678 5 Objective Function 6 Profit 9 10 Constraints 11 12 Demand Constraints 13 XA 14 XB 15 XC 16 xD 17 XE 18 xF C D E F G H J K L M N P Q =607*B3+3*C3+12*D3+6*E3+18*F3+17*G3 B A B C D E 1 1 1 1 1 LHS 19 Testing Equipment Time Constraints 20 T1 21 T2 22 T3 23 24 25 26 Decision Variables are Integer 27 Non-Negativity 28 VI VI VI VI VI VI VI VI RHS |=607*B3+3*C3+12*D3+6*E3+18*F3+17*G3 644 622≤ 100 80 F 1 X_A0X_BOX_C0X_D>=0X_E=0X_F>=0 File Home Insert Draw Design Layout References Mailings Review View Help Х Aptos Display (Head | 11 ▾ Aˆ A Paste BIU ab X x² A Aa A A ▾ ་ Normal No Spacing Heading Heading 2 Title H v Clipboard ✓ Font ✓ Paragraph √☑ Styles QUESTION 1 - LINEAR PROGRAMMING An auto part manufacturer sells six different parts to automobile companies: spot lights (A), break lights (B), headlights (C), thermostat (D), fan ditch (E), and battery (F). Demand is expected to be within 2,000, 1,500, 1,800, 1,200, 1,000 and 1,000 units of each of the auto parts, respectively. The table that follows summarizes the revenues and material costs for each product: Auto Parts Produced Price per Unit Material Cost per Unit A B C D E F 200 120 180 200 430 260 35 25 40 45 170 60 Each of these auto parts needs to be tested before being sold. Specifically, there are three different tests the protocol requires each part passes, before completing the quality check. Appropriate testing equipment is required for each test: T1, T2 and T3. Equipment T1 and T2 are available 100 hours per week each, while T3 is available only 80 hours per week. The time (in minutes) required per device for each of the three tests is reported in the following table: Electronic Devices Produced A B C D E F Test on T1 7 3 12 6 18 17 Test on T2 2 5 3 2 15 17 Test on T3 5 1 3 2 9 2 Specialized personnel is required to operate each of the test equipment. The variable labour costs are £16 per hour for equipment T1, £12 per hour for T2, and £20 per hour for T3. A) Considering the manufacturer intends to maximize profit, write a linear program for this problem and find a solution with Excel Solver. Reflect on whether to impose a constraint on the nature of the decision variables. K>> Comments Find ▾ Editing Share Ө Replace Select Editor Dictate Add-ins Editing Voice Editor Add-ins

B20 × ✓ fx A 1 Decision Variables 2 Products 12345678 5 Objective Function 6 Profit 9 10 Constraints 11 12 Demand Constraints 13 XA 14 XB 15 XC 16 xD 17 XE 18 xF C D E F G H J K L M N P Q =607B3+3C3+12D3+6E3+18F3+17G3 B A B C D E 1 1 1 1 1 LHS 19 Testing Equipment Time Constraints 20 T1 21 T2 22 T3 23 24 25 26 Decision Variables are Integer 27 Non-Negativity 28 VI VI VI VI VI VI VI VI RHS |=607B3+3C3+12D3+6E3+18F3+17G3 644 622≤ 100 80 F 1 X_A0X_BOX_C0X_D>=0X_E=0X_F>=0 File Home Insert Draw Design Layout References Mailings Review View Help Х Aptos Display (Head | 11 ▾ Aˆ A Paste BIU ab X x² A Aa A A ▾ ་ Normal No Spacing Heading Heading 2 Title H v Clipboard ✓ Font ✓ Paragraph √☑ Styles QUESTION 1 - LINEAR PROGRAMMING An auto part manufacturer sells six different parts to automobile companies: spot lights (A), break lights (B), headlights (C), thermostat (D), fan ditch (E), and battery (F). Demand is expected to be within 2,000, 1,500, 1,800, 1,200, 1,000 and 1,000 units of each of the auto parts, respectively. The table that follows summarizes the revenues and material costs for each product: Auto Parts Produced Price per Unit Material Cost per Unit A B C D E F 200 120 180 200 430 260 35 25 40 45 170 60 Each of these auto parts needs to be tested before being sold. Specifically, there are three different tests the protocol requires each part passes, before completing the quality check. Appropriate testing equipment is required for each test: T1, T2 and T3. Equipment T1 and T2 are available 100 hours per week each, while T3 is available only 80 hours per week. The time (in minutes) required per device for each of the three tests is reported in the following table: Electronic Devices Produced A B C D E F Test on T1 7 3 12 6 18 17 Test on T2 2 5 3 2 15 17 Test on T3 5 1 3 2 9 2 Specialized personnel is required to operate each of the test equipment. The variable labour costs are £16 per hour for equipment T1, £12 per hour for T2, and £20 per hour for T3. A) Considering the manufacturer intends to maximize profit, write a linear program for this problem and find a solution with Excel Solver. Reflect on whether to impose a constraint on the nature of the decision variables. K>> Comments Find ▾ Editing Share Ө Replace Select Editor Dictate Add-ins Editing Voice Editor Add-ins

Economics Today and Tomorrow, Student Edition

1st Edition

ISBN:9780078747663

Author:McGraw-Hill

Publisher:McGraw-Hill

Chapter5: Buying The Necessities

Section: Chapter Questions

Problem 20AA

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