$5\mathrm{.}1$ 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:

$6\mathrm{.}1$ Consider exercise $3\mathrm{.}1.$

$($a$)$ Consider a bicriteria problem where the objectives are to minimize total cost $(f_1)$

and minimize total backorders $(f_2).$ Suppose the weights of importance for the

normalized objective values are $(0\mathrm{.}4,0\mathrm{.}6),$ respectively. Use an additive utility

function for the MOLP problem to determine the optimal plan.

$($b$)$ Consider three linear objectives: total cost, total backorder, and total firing. Suppose

the weights of importance for the normalized objective values are $(0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}5),$

respectively. Use an additive utility function for the MOLP problem to determine

the optimal plan.