A LP problem has three constraints: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≤ 90 and the non-negativity constraints. The objective is to Maximize X.
1. Write the problem in standard form. (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. Write the initial simplex table and label it Simplex Table 3A.1.
4. After creating Simplex Table 3A.1, find the entering variable using the Cj-Zj values and type it here.
5. What is the leaving variable? (Show MRR calculations.)
6. Write the elementary row operations for finding the new row __.
7. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
8. If row __ changes, write the elementary row operations for finding the new row __. If row __ does not change, explain why it does not change.
9. Write the new table and label it Simplex Table 3B.2.
10. Is there an entering variable for the next table? If so, what is the entering variable? If not, explain what this means.
11. What is the largest quantity of X that can be made without violating any of these constraints? Explain your answer.