A linear programming computer package is needed.

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data $($in price per unit$)$ are as follows.

Component Supplier

$123$

$1$ $$11$ $$12$ $$13$

$2$ $$9$ $$10$ $$9$

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component $1,$ component $2,$ or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows.

Supplier $123$

Capacity $400800600$

$($a$)$

If the Edwards production plan for the next period includes $800$ units of component $1$ and $600$ units of component $2,$ what purchases do you recommend? That is$,$ how many units of each component should be ordered from each supplier?

Component $1,$ Supplier $1$

units

Component $1,$ Supplier $2$

units

Component $1,$ Supplier $3$

units

Component $2,$ Supplier $1$

units

Component $2,$ Supplier $2$

units

Component $2,$ Supplier $3$

units

$($b$)$

What is the total purchase cost $($in $$)$ for the components?

$