4300

Consider a toy company, that manufactures 6 different products. The following LP that maximizes the prot in dollars by selling 6 different products is based on the data collected from the company. The first constraint represent the raw material resource limit in cc units, and the second constraint represents the production equipment capacity limit in hours. The next six constraints represents the minimum production quantity on each of the six products.
max : 12 x1 + 7 x2 + 5×3 + 6 x4 + 7 x5 + 8 x6
s.t. 3 x1 + 4 x2 + 5 x3 + 7 x4 + 6 x5 + 1 x6 =800
x1 + x2 + x3 + x4 + x5 + x6 =1000
x1 =10
x2 =9
x3 =12
x4 =8
x5 =7
x6 =10
x1, x2, x3, x4, x5, x6 =0
1. What happens to the feasible region, if the RHS on resource constraint is increased by +1.
2. What happens to the optimal objective function value, if the RHS on resource constraint is increased by +1.
3. What happens to the feasible region, if the RHS on capacity constraint is increased by +1
4. What happens to the optimal objective function value, if the RHS on capacity constraint is increased by +1.
5. If the dual optimal solution to the above LP is [8, 0, -12, -25, -35, -50, -41, 0]T
, then will there be any change in any of your earlier answers (for Part-1 to 4). Explain.
6. Find the primal optimal solution without solving the primal.
7. What is the primal optimal objective function value.
8. Identify any excess resource or equipment hours available with the company, while operating at the optimal levels.
9. Assume that the local market has following options:
• Buy/Sell the raw material for a price of 8 dollars per cc.
• Lease/Rent production equipment hours for a price of 8 dollars per hour.
Management has following two new projects, which one will you pick rationally to maximize the
overall profit:
• Sell the entire available resources and lease the entire production equipment hours.
• Lease the excess equipment hours, and continue with the optimal levels.
10. What will happen to the overall profit, if the management plans to buy raw material from the local market. Explain.

Attachments:

hw.docx