3. Another problem from HW 3: Max 2C+3W st 2 25 C+2W 560 Constraint 1 5C + 3W S 150 Constraint 2 2.5C Constraint 3 CW 20 a. Starting from the algebraic form above, rewrite the linear program in STANDARD form (that is, including slack and surplus variables. b. The optimal solution was found to be C=172, W=21. Find the slack or surplus for each of constraints 1 through 3 by plugging the optimal solution into each of the constraints and solving for the s c. Recall that binding constraints must have slack or surplus equal O. Are your results from b. consistent with that? (if not check your algebra) d. Which constraints have non-zero slack or surplus? Are those values slack, or are they surplus? Explain how you can tell which is which. 4. Remember in HW 3 you solved the problem above a second time, but using the minimum for the objective function rather than the max as in problem 1. a. Rewrite the LP from problem 1 in STANDARD form, but now using minimum for your objective function rather than max. Other than that change, will there be any other differences in the standard form between problem 1 and the standard form you write below? b. The optimal solution was different between the minimum and maximum versions of the problem in HW 3. The optimal solution for the minimum version was C = 10 and W=0. For each of the constraints 1-3, find the new values of the slack or surplus by plugging in the optimal solution for the minimum problem c. What were the binding constraints for this minimization problem (see HW 3 solutions if you don't remember)? Are the slack/surplus values for the binding constraints here O? (If they are not, a mistake was made somewhere.) d. Which constraints have non-zero slack or surplus? Are the numbers you got slack, or are they surplus? How can you tell