Intro to Optimization: Linear Programming Solutions - Edubirdie

University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
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70

Pages:

1
Author:

iwblogjre

Lecture Check Problems: Lecture 1 Solutions: 1. max z = 30 x1 + 100 x 2 x1 + x 2 ≤7 (Land Constraint) s.t. 4 x1 + 10 x 2 ≤40 (Labor Constraint) 10 x1 ≥30 (Government Constraint) x1 ≥ 0, x 2 ≥ 0 2a. No, government constraint is violated. 2b. No, Labor constraint is not satisfied. 2c. No, x 2 ≥ 0 is not satisfied. 2d. Yes, all constraints and sign restrictions are satisfied. 3. 1 bushel of corn uses 1/10 acre of land and 4/10 hours of labor while 1 bushel of wheat uses 1/25 acre of land and 10/25 hours of labor. This yields the following formulation: max z = 3 x1 + 4 x 2 s.t. x1 /10 + x 2 /25 ≤ 7 (Land Constraint) 4 x1 /10 + 10 x 2 /25 ≤ 40 (Labor Constraint) x1 ≥ 30 (Government Constraint) x1 ≥ 0, x 2 ≥ 0 x1 = Number of Type 1 Trucks produced daily 4. x 2 = Number of Type 2 Trucks produced daily Expressing profit in hundreds of dollars we obtain the following formulation: max z = 3 x1 + 5 x 2 x1 /800 + x 2 /700 ≤ 1 (Paint Shop Constraint) s.t. x1 /1500 + x 2 /1200 ≤ 1 (Engine Shop Constraint) x1 ≥ 0, x 2 ≥ 0

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