# HELP A.S.A.P. PLEASE: linear programming-maths

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A company makes tennis and squash rackets. Each tennis racket requires two units of aluminum and one unit of nylon. Each squash racket requires 1.8 units of aluminum and 0.8 units of nylon. The company has 1000 units of aluminum and 800 units of nylon available. The company is not able to manufacture more than 550 rackets in total but must manufacture at least twice as many tennis rackets as squash rackets. The profit on each tennis racket and squash racket is \$7 and \$9 respectively.

Let and represent the number of each type of racket made in order to maximize profit.

Formulate the above information as a Linear Programming Problem by determining
i. the objective function

ii. the linear constraints

• HELP A.S.A.P. PLEASE: linear programming-maths -

The objective function in this case is to calculate the profit.
s=number of squash rackets (made and) sold.
t=number of tennis rackets (made and) sold.

From "The profit on each tennis racket and squash racket is \$7 and \$9 respectively"
we can say that the objective function, P(s,t)=7t+9s

I will show how to compose the two constraints concerning aluminium and nylon.

"Each tennis racket requires two units of aluminum and one unit of nylon. Each squash racket requires 1.8 units of aluminum and 0.8 units of nylon. The company has 1000 units of aluminum and 800 units of nylon available. "
This translates to:
2t+1.8s ≤ 1000,
2t+0.8s ≤ 800

I will leave it to you to complete the other constraints

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