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 A B C D E F Price per Unit 200 120 180 200 430 260 Material Cost per Unit 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. 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.
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 |
|||||
|
|
A |
B |
C |
D |
E |
F |
|
Price per Unit |
200 |
120 |
180 |
200 |
430 |
260 |
|
Material Cost per Unit |
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.
- 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.
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