Using the following factor ratings, determine which location alternative $($X$,$ Y$,$ or Z$)$ should be chosen on the basis of maximum composite score.

$$Location Score

Factor

Weight

X

Y

Z

Convenience

$0\mathrm{.}15$

$80$

$70$

$60$

Parking facilities

$0\mathrm{.}27$

$88$

$76$

$92$

Display area

$0\mathrm{.}18$

$94$

$88$

$90$

Shopper traffic

$0\mathrm{.}20$

$98$

$86$

$80$

Operating costs

$0\mathrm{.}10$

$86$

$90$

$85$

Neighborhood

$0\mathrm{.}10$

$82$

$83$

$72$

$$

Rent and equipment costs $($all fixed costs$)$ would be $$5,000$ per month for Location A$,$ $$5,500$ for location B$,$ and $$6,000$ for Location C$.$

$$

Required :

a$.$ Determine the volume $($Q$)$ necessary for each location to realize a monthly profit of $$15,000.$ Rounded to the nearest whole number.

b$.$ If expected sales $($in units$)$ at A$,$ B$,$ and C are $22,000$ per month, $24,000$ per month, and $26,000$ units per month, respectively, which location would yield the highest profits.$$

Hint:$$ You would need to compute the profit for each location first before you selected the $$best$$ location.