Question

27. MANUFACTURING A shoe manufacturer makes outdoor

Answer 1

Answer:

Maximum profit = $840

For maximum profit, number of outdoor shoes will be 12 and indoor shoes 16.

Step-by-step explanation:

Manufacturer makes outdoor and indoor soccer shoes.

The company has 40 hours for step one and 60 hours available for step two.

Let the company manufacture number of outdoor shoes = x and indoor shoes = y

For each pair of outdoor shoes,

It takes 2 hours in step 1 and 1 hour in step 2 and produces a profit of $20.

For each pair of indoor shoes,

It takes 1 hour in step one and 3 hours in step 2 and produces a profit of $15.

For step one inequality will be,

2x + y ≤ 40 ------(1)

For step two inequality will be,

x + 3y ≤ 60 ------(2)

Multiply inequality (2) by 2 and subtract it from inequality (1).

2(x + 3y) - (2x + y) ≤ 60(2) - 40

2x + 6y - 2x - y ≤ 120 - 40

5y ≤ 80

y ≤ 16

Now from equation (2)

x + 3(16) ≤ 60

x + 48 ≤ 60

x ≤ 60 - 48

x ≤ 12

To manufacture 12 pairs of outdoor shoes, profit produced = $20×12

= $240

To manufacture 16 indoor shoes, profit earned = $15×16

= $240

Maximum profit produced = $240 + $240 = $480