Question

question 18 (5 points) retake question interpret the meaning of the minimum value in terms of the objective function in the following situation. you are starting a business and you want to minimize the cost of healthcare insurance that you provide for your employees. the constraints for healthcare benefits are graphed below. the objective function is c = 200x + 150y where c represents total cost of healthcare expenses for employees per month, x represents the number of full - time employees you have, and y represents the number of part - time employees that you have. you should hire 0 full - time employees and 20 part - time employees to have a minimum healthcare cost of $1500. you should hire 20 full - time employees and 60 part - time employees to have a minimum healthcare cost of $13000. you should hire 0 full - time employees and 80 part - time employees to have a minimum healthcare cost of $12000. you should hire 10 full - time employees and 0 part - time employees to have a minimum healthcare cost of $2000.

Explanation:

Step1: Recall objective - function formula

The objective function is $C = 200x+150y$, where $C$ is the total cost, $x$ is the number of full - time employees, and $y$ is the number of part - time employees.

Step2: Check each option

Option 1:

If $x = 0$ and $y=20$, then $C=200\times0 + 150\times20=3000
eq1500$.

Option 2:

If $x = 20$ and $y = 60$, then $C=200\times20+150\times60=4000 + 9000=13000$.

Option 3:

If $x = 0$ and $y = 80$, then $C=200\times0+150\times80 = 12000$.

Option 4:

If $x = 10$ and $y = 0$, then $C=200\times10+150\times0=2000$.

We need to find the minimum value among these valid - point calculations. Among the calculated costs $3000$, $13000$, $12000$, and $2000$, the minimum cost is $12000$ which occurs when $x = 0$ and $y = 80$.

Answer:

You should hire 0 full - time employees and 80 part - time employees to have a minimum healthcare cost of $12000$.