GRADED PROBLEMS

Problem $1$

Consider the following optimization problem:

min $4$x $+2$y

s$.$t$.3$x $+3$y $60$

$$x $+5$y $25$

$3$x $15$

x$,$ y $0$

a$.$ Solve this problem using LINGO. Please give the optimal solution as well as the

optimal objective function value $($you do not need to print the output; writing and

explaining your answer is enough for all parts of this problem$).$

b$.$ Suppose we changed this problem to an integer program $($i$.$e$.,$ we restricted x and

y to take integer values$).$ Would the optimal solution change? Why or why not?

c$.$ How much slack or surplus is there in each of the constraints at the LP optimal

solution?

d$.$ Change the objective function from a minimization to a maximization problem.

What does LINGO tell you about the optimal solution now?

e$.$ Keep the objective function as a maximization problem, add the constraint x $$

$20,$ and resolve the problem. What are the optimal solution and the optimal

objective function value now?

f$.$ From the results for part e$.,$ which constraints are binding at the optimal solution?