$5\mathrm{.}1$ Consider a company that produces three types of car tires: $C{T}_1,C{T}_2,$ and $C{T}_3.$ Currently

there are $75,90,$ and $80$ units $($in thousands$)$ regular production workforce per month

for products $C{T}_1,C{T}_2,$ and $C{T}_3,$ respectively. The costs for the tires are as follows.

The resource limitations $($in thousands$)$ of the company are listed below.

Determine the production plan for the next three months, where the forecasted demand

$($in thousands$)$ for each product for each month as follows:

$5\mathrm{.}3$ Consider exercise $5\mathrm{.}1.$ Suppose that regular production can be conducted by the same

workforce for different products. Find the total cost and the value of decision variables.

Compare this solution to the solution of exercise $5\mathrm{.}1.$