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
