How many of each type should the company produce per day to maximize profit?

Question

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 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. If the company profits are $28.50 for the cord-type model and $57.00 for the cordless model

Scenario #1 (with the smaller number of cord-type trimmers)

corded models:______

cordless models:_____

Scenario #2 (with the larger number of cord-type trimmers):

corded models:_____

cordless models:____

Answer 1

X is cordless

Y is cord type

2x + 4y <= 800 <--- time constraint

x + 2y <= 400

x+y <= 300

Objective function is : 28.5x + 57y

the critical points are (0,200)

(200,100)

(300,0)

and (0,0) which is useless

(0,200) and (200,100) results in the same max of $11400