A company makes counters and doors. Each counter can be sold for $30 and each do

Question

A company makes counters and doors. Each counter can be sold for $30 and each door for $18. The company afford to spend up to 70 hours and 50 hours per week on woodworking and painting,respectively. The time and cost required by each product is shown in the table below. Customer demand requires that he makes at least three times as many doors as counters. Counter take up four times as much storage space as door and there is room for at most four counters each week. How many counters and doors should the company manufacture each week to optimize the profit? door counter woodworking 3hrs 1.5hrs painting .75hrs 1hrs cost $10 $20

Explanation / Answer

Counter sold for $30

Door sold for $18

Time spent on woodworking = 70 hrs per week

Time spent on painting = 50 hrs per week

Woodworking time on door = 3 hrs

Woodworking time on counter = 1.5 hrs

Painting time on door = 0.75 hrs

Painting time on counter = 1 hr

Cost for door = $10

Cost for Counter = $20

No. of doors = x

No. of counters = y

x>=3y

y<=4

x<=16

x>=0 , y>=0 since the no. of doors and counters cant be negative

Profit equation = 10x + 8y = P

3x+1.5y<=70

0.75x+y<=50

Plotting all the graphs we get corner points (0,0) , (12,4) , (16,4) , (16,4)

Therefore x=16 , y=4 gives the maximum profit
That is $192

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