Independent exercises

For exercises 2–5, baseline: maximize 8a+6b−10yA−8yB; 2a+b≤12, a+b≤10, a≤6yA, b≤8yB; a,b≥0 continuous; yA,yB binary. All money: $1,000/week. Reset to baseline for each question.

1. Integer production

Maximize 3x+2y with x+y≤4, 2x+y≤6.5, and nonnegative integer x,y. Find the optimum and verify it by enumeration.

Write: model change → plan → objective → feasibility checks → conclusion.

2. Sales cap 6

Reset the plant model to baseline, then replace a+b≤10 with a+b≤6. Compare all four opening patterns.

Write: model change → plan → objective → feasibility checks → conclusion.

3. At most one line

Use baseline data and add yA+yB≤1. What is the best opening and production plan?

Write: model change → plan → objective → feasibility checks → conclusion.

4. A module costing 8

Use baseline plant data plus an optional module adding 4 labor units. Its weekly cost is 8. Compare buy and do not buy.

Write: model change → plan → objective → feasibility checks → conclusion.

5. A minimum batch of 4

Reset to baseline and add a≥4yA. Compare opening patterns and determine the optimum.

Write: model change → plan → objective → feasibility checks → conclusion.

6. A remaining optimality gap

A maximization MILP has feasible incumbent value 46 and a valid global upper bound 48. What can be concluded?

Write: model change → plan → objective → feasibility checks → conclusion.

Open worked solutions after attempting the questions