question 4 (5 points)\ninterpret the meaning of the minimum value in terms of the objective function in the…

question 4 (5 points)\ninterpret 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 = 500x + 300y 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.\nyou should hire 10 full - time employees and 0 part - time employees to have a minimum healthcare cost of $5500.\nyou should hire 20 full - time employees and 60 part - time employees to have a minimum healthcare cost of $34,000.\nyou should hire 60 full - time employees and 0 part - time employees to have a minimum healthcare cost of $4500.\nyou should hire 0 full - time employees and 20 part - time employees to have a minimum healthcare cost of $5000.

question 4 (5 points)\ninterpret 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 = 500x + 300y 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.\nyou should hire 10 full - time employees and 0 part - time employees to have a minimum healthcare cost of $5500.\nyou should hire 20 full - time employees and 60 part - time employees to have a minimum healthcare cost of $34,000.\nyou should hire 60 full - time employees and 0 part - time employees to have a minimum healthcare cost of $4500.\nyou should hire 0 full - time employees and 20 part - time employees to have a minimum healthcare cost of $5000.

Answer

Brief Explanations:

The objective function $C = 500x+300y$ represents the total monthly cost of healthcare for employees, with $x$ full - time and $y$ part - time employees. To find the minimum cost, we evaluate the function at the corner points of the feasible region (the shaded area). The corner points are likely $(0,20)$, $(10,0)$ etc. We substitute these points into the objective function. For $(10,0)$, $C=500\times10 + 300\times0=5000$. For $(0,20)$, $C = 500\times0+300\times20 = 6000$. The minimum cost occurs when $x = 10$ and $y = 0$.

Answer:

You should hire 10 full - time employees and 0 part - time employees to have a minimum healthcare cost of $5000.