(d)

Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 140 units of product 1, 145 units of product 2, or 150 units of product 3. (Let

P_i =

units of product i produced and

y_i

be the 0-1 variable that is one if any quantity of product i is produced and zero otherwise, for

i = 1, 2, 3.)

What is the objective function of the mixed-integer linear program?

Max

In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program?

s.t.units of Product 1 produced

units of Product 2 produced

units of Product 3 produced

P₁, P₂, P₃ 0; y₁, y₂, y₃ = 0, 1

(e)

Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit (in dollars) contribution?

(P₁, P₂, P₃, y₁, y₂, y₃) =

with profit $

.