A linear programming computer package is needed. supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Min $\backslash (\backslash )$

Cutting constraint

Milling constraint

Shaping constraint

Frame constraint

Support constraint

Strap constraint

$\backslash ($ F M$,$ F P$,$ S M$,$ S P$,$ T M$,$ T P $\backslash$geq $0\backslash )$

How many of each component should be manufactured and how many should be purchased? $($Round your answers to the nearest whole number.$)$

$\backslash (($F M$,$ F P$,$ S M$,$ S P$,$ T M$,$ T P$)=(\backslash$quad$)\backslash )$

$($b$)$ What is the total cost $($in $\backslash (\backslash$$ $\backslash ))$ of the manufacturing and purchasing plan?

$\backslash (\backslash$$ $\backslash )$

$($c$)$ How many hours of production time are used in each department? $($Round your answers to two decimal places.$)$

$($d$)$ How much $($in $\backslash (\backslash$$ $\backslash ))$ should Frandec be willing to pay for an additional hour of time in the shaping department?

$\backslash$$

$($e$)$ Another manufacturer has offered to sell frames to Frandec for $\backslash (\backslash$$ $45\backslash )$ each. Could Frandec improve its position by pursuing this opportunity? Why or why not? $($Round your answer to three decimal places.$)--$ Select$---.$ The reduced cost of indicates that the solution $-$ Select $\backslash (-\backslash$vee $\backslash )$ be improved.