Question: Given the following all-integer linear program: MAX 15 H + 2 K s.t. 7 H + K < 23 3 H - K < 5

Given the following all-integer linear program:

MAX	15 H + 2 K
s.t.	7 H + K < 23
	3 H - K < 5
	H, K 0 and integer

a. Solve the problem (using SOLVER) as an LP, ignoring the integer constraints. What are the values of H, K, and the objective function?

b. What solution is obtained by rounding all fractional decision variables (round fractions >0.5 UP and <0.5 DOWN)? What are the values of H, K, and the objective function? Is this solution feasible? Is it the optimal integer solution?

c. What solution is obtained by rounding the decision variables DOWN? What are the values of H,K, and the objective function? Is this solution feasible? Is it the optimal integer solution?

d. Resolve original problem using SOLVER with the Integer requirements included. What are the values of J, M, and the objective function?

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