3. [30%] Consider the following linear program modelling the profit obtained from the sale of three different products I1, I2 and 13, along with constraints: Max 2x1 + 412 + 7.23 subject to: C: I1 + 12 + 3 310 C3: 2x1 + 4.02 + 4.03 > 330 21, 22, 23 > 0 The problem was solved using a computer program and the following output was obtained: Allowable Allowable Variable Value Reduced Cost Increase Decrease 31 0.000 -3.500 3.500 50.000 0.000 3.000 7.000 55.000 0.000 3.000 22 13 Constraint Slack/Surplus Dual Price 1 0.000 10.000 2 0.000 -1.500 3 90.000 0.000 Constraint right-hand side (RHS) sensitivity: Constraint Allowable Increase Current RHS Allowable Decrease 1 50.000 105.000 22.500 2 110.000 310.000 100.000 3 90.000 330.000 (a) Create an Excel linear program and solve to confirm the optimal solution found by the previous computer program. (You do not need to perform the sensitivity analysis) (b) Which constraints are binding? (c) Suppose the profit from x2 is increased to $8. Is the above solution still optimal? Why? (d) We are not producing any of product 21. What is the minimum increase in the profit of xi that would compel us to consider producing at least one x? (e) Constraint 1 depicts the availability of a certain resource. If that resource was increased from 105 to 125, would this constraint be still binding? (f) Further research has shown that constraint 3 should be 2x1 + 4.22 + 5x3 > 330 What steps can you take to correct your existing linear program to in- clude this new information