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A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day. If the company profits for the cord-type model for $36.50 and the cordless model for $109.50, how many of each type should it produce per day to maximize profits?

Respuesta :

samuelonum1

Answer:

P=$14600

The company should produce

100cordless and 100 cord-type

Step-by-step explanation:

This is a linear programming question

let the cordless trimmer be X

and the cord type be Y

the objective function is

maximize

36.50x+109.50y=P

constraints

2X+6Y<=600-----1

X+Y=200-----------2

solve 1 and 2 simultanouesly

mutiply  eqn 2 by 2 we have

2x+6y=600-------1

2x+2y=200--------3

subtract the eqns 3 from 1

4y=400

y=100

put y=100 in eqn 2 we have

x+100=200

x=200-100

x=100

36.50x+109.50y=P

36.50(100)+109.50(100)=P

 3650+10950=P

P=$14600

The company should produce

100cordless and 100 cord-type

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