Given this LP Model below:

Max $z=4x+5y$

Subject $to$

$2x+2y22$

$-1x+1y4\frac{?}{b}$

$ar(y)=7$

$1x-5y0$

$x0,y0$

a$)$ Solve for the quantities of $x$ and $y$ which will maximize $Z.$ The $x=q,$ The $y=$ type your answer The $y=$ type your answer

$$

b$)$ What is the maximum value of Z $?$ The $Z=-$

Fill in the Blank $6$ points

A Company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used $6$ workers, who produced an average of $85$ carts per hour. Workers receive $$13$ per hour, and machine coast was $$45$ per hour With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $$19$ per hour while output increased by four carts per hour.

a$)$ Compute the multifactor productivity $($NFP$)($labor plus equipment$)$ under the After buying the new equipment. The MFP $($carts$/$S$)=$ type your answer. $($round to $4$ decimal places$).$

b$)$ Compute the $\%$ growth in productivity between the Prior to and after buying the new equipment. The growth in productivity$=$ typeyour answer. $\%($round to $2$ decimal places$)$