Answer:
To maximize profits;
96 t-shirts should be produced
85 hats should be produced
The profit from the t-shirts is $348
The profit from the hats is $425
Step-by-step explanation:
The given information are;
The amount of profit per t-shirt = $4
The amount of profit per t-shirt = $5
The time it takes to print a t-shirt = 10 minutes
The time it takes to dry the printed t-shirt = 15 minutes
The time it takes to print a hat = 16 minutes
The time it takes to dry the printed hat = 12 minutes
The amount of time available for printing = 20 hours = 1200 minutes
The amount of time available for drying = 20 hours = 1200 minutes
Therefore, we have;
The total number of t-shirts that can be printed in 20 hours = (The amount of time available for printing)/(The time it takes to print a t-shirt)
The total number of t-shirts that can be printed in 20 hours = (1200 minutes)/(10 minutes)
The total number of t-shirts that can be printed in 20 hours = 120 t-shirts can be printed
The total number of t-shirts that can be dried in 20 hours = (The amount of time available for drying the t-shirts)/(The time it takes to dry a t-shirt)
The total number of t-shirts that can be dried in 20 hours = (1200 minutes)/(15 minutes) = 80 t-shirts can be dried
The total number of hats that can be printed in 20 hours = (The amount of time available for printing)/(The time it takes to print a hat)
∴ The total number of hats that can be printed in 20 hours = (1200 minutes)/(16 minutes) = 75 hats can be printed
The total number of hats that can be dried in 20 hours = (The amount of time available for drying the hats)/(The time it takes to dry a hat)
∴ The total number of hats that can be dried in 20 hours = (1200 minutes)/(12 minutes) = 100 hats
Therefore, given that only 80 t-shirts can be dried in 20 hours, we have;
The total number of t-shirts to be produced = 80 t-shirts
The profit made from the shirts is 80 × $4 = $320
Also, given that only 75 hats can be dried in 20 hours, we have;
The total number of t-shirts to be produced = 75 hats
The profit made from the shirts is 75 × $5 = $375
However, to maximize profit, we have;
Total time to print and dry the t-shirts = 1200 + 1200 = 2,400 minutes
Therefore, whereby X number of t-shirts can be produced in the total time, we have;
10·x + 15·x = 2,400 minutes
25·x = 2,400 minutes
x = 2,400 minutes/25 = 96 t-shirts should be produced
Profit = $4 × 96 = $348
Similarly, for the hat, we have;
16·x + 12·x = 2,400 minutes
28·x = 2,400 minutes
x = 2,400 minutes/28 ≈ 85 hats should be produced (rounding down)
Profit = $5 × 85 = $425.
