Forumulate the following as a linear program. Jessica\'s aircraft muffler manufa

Question

Forumulate the following as a linear program.

Jessica's aircraft muffler manufacturers have 1000 linear feet of steal on hand to make to manufacture the three top selling muffler sets. Super mufflers (S) provide $35 dollar profit and common mufflers (c) mufflers' profit margin is $31, while the deluxe (D) muffler set provides a $40 profit margin. It takes 31 hours to make the super muffler, 29 hours to manufacture the common muffler and 40 hours to build the deluxe muffler. If Jessica is limited to 200 hours a month what is the optimum combination of mufflers to maximize his profits?

Assume it takes 1 linear foot of steel to produce each product.

a) Define the decision variables of jessica’s model as completely as you can.

b) Write the objective function for this model.

c) Write all constraints of the model.

Explanation / Answer

a) Decision variables of Jessica's model -

S = Number of Super mufflers

C = Number of Common mufflers

D = Number of Deluxe mufflers

b) The objective function for the model is -

Maximize Profit Z = 35S+31C+40D

c) Constraints of the model -

S+C+D <= 1000 --> Linear feet of steel capacity

31S+29C+40D <= 200 --> Hours constraint

S,C,D >= 0 --> Non-negativity constraints

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