A manager must decide on the mix of products to produce for the coming week. Each unit of Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute for packing. Each unit of Product B requires two minutes per unit for molding, four minutes for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have contributions of $1.50 per unit.
1. Formulate the problem as a LP and write the linear programming model here. (Include definitions of decision variables, objective function and constraints.)
2. Solve the problem using QM for Windows. Paste image of Linear Programming Results window and Solution List window here.
3. What combination of A and B will maximize contribution, and what is the maximum possible contribution?
4. Write the problem in standard form. (Include definitions of decision variables, objective function and constraints.)
5. Write the initial simplex table and label it Simplex Table 2A.1.
6. After creating Simplex Table 2A.1, find the entering variable using the Cj-Zj values and write it here.
7. What is the leaving variable? (Show MRR calculations.)
8. Write the elementary row operations for finding the new row __.
9. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
10. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
11. Write the new table and label it Simplex Table 2B.2.
12. What is the entering variable?
13. What is the leaving variable?
14. Write the elementary row operations for finding the new row __.
15. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
16. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
17. Write the new table and label it Simplex Table 2C.3.
18. Is there an entering variable? If not, explain what this means.