$q,$ WS $2\mathrm{.}3-2\mathrm{.}42$ of $2$

The prices for Freddy's Filing Cabinets are: $$80$ for $2-$drawer cabinets, $$120$ for $3$ drawer cabinets, and $$160$ for $4-$drawer cabinets. The first table below gives sales numbers for July; the second table gives the price for each size.

Freddy's Filing Cabinets $-$ sales for July $($Matrix F$)$

$\backslash$table$[[,2-$drawer,$3-$drawer,$4-$drawer$],[$Store $1,30,20,40],[$Store $2,50,10,60],[$Store $3,25,15,35]]$

Cabinet Prices $($Matrix P$)$

$\backslash$table$[[,2-$drawer,$3-$drawer,$4-$drawer$],[$Price$,80,120,160]]$

$($a$)$ Write out and label the matrices for the product matrix $F{P}^T.$ Find the product matrix. & interpret.

$($b$)$ Write out and label the matrices for the product matrix $P{F}^T.$ Find the product matrix. & interpret. Compare with the product matrix in $($a$).$

$($c$)$ Write out and label the matrices for the product matrix $PF?$ Find the product matrix. & compare with $($a$)$ and $($b$).$

$($d$)$ What was Store $1\text{'}$s total revenue for July?

$($e$)$ What was Store $2\text{'}$s total revenue for July?

$($f$)$ What was Store $3\text{'}$s total revenue for July?

Use the simplex method to s$$lve the linear programming problem.

Maximize $z=4x_1-3x_2+2x_3$

subject $to2x_1-x_2+8x_{3}46$

$,4x_1-5x_2+6x_{3}72$

$,2x_1-2x_2+6x_{3}34$

$,x_{1}0,x_{2}0,x_{3}0$

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The maximum is $$ when $x_1=,x_2==x_3=s_1=s_2=$ and $s_3=.$

B$.$ There is no maximum.