A clothing design company pays two different people to design its T-shirts.
The company pays person A $8 an hour and pays person B $12. Person A
cannot work more than twice as many hours as person B, but they cannot
work more than 20 hours total. Person A makes the company a profit of $10
an hour, and person B makes the company a profit of $20 an hour. If the
company wants to make at least $150 in profit, which value will minimize the
cost to the company? (Each point is (a, b), where a is the hours person A
works and b is the hours person B works.)

A. (13.33, 6.67)
B. (7.5, 12.5)
C. (0,20)
D. (0, 7.5)

The objective function is simply an equation that represents the goal production capability that relates to maximizing profits in relation to manufacturing.

Given data;

Payout of person A= $8 an hour

Payout of person B= $12 an hour

Working hour of the person A ,y<2x

x+y=20

For the minimum value;y=2x

x+y=20

x+2x=20

3x=20

x=6.66

A work 6.66 hour. While B works 13.33 hours.

Person A makes the company a profit of = $10 an hour

Person B makes the company a profit of $20 an hour

Total profit by A = time ×profit/time

Total profit by A =6.66×10

Total profit by A =66.6

Total profit by B = time ×profit/time

Total profit by A =13.33×20

Total profit by A =266.6

If the company wants to make a profit of $150. Person B will work for 7.5 hours at the cost of the $20 an hour.

Hence,option D is correct.

To learn more about the objective function, refer to the link;

https://brainly.com/question/15830007

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