Limited Resources

Maria Pajet, a regional sales representative for UniTec Systems, Inc., has been working about $80$ hours per week calling on a total of $123$ regular customers each month. Because of family and health considerations, she has decided to reduce her hours to a maximum of $160$ per month. Unfortunately, this cutback will require Maria to turn away some of her regular customers or$,$ at least, serve them less frequently than once a month. Maria has developed the following information to assist her in determining how to best allocate time:

Customer Classification

Large

Business Small

Business Individual

Number of customers $83580$

Average monthly sales per customer $$4,500$ $$2,400$ $$1,100$

Commission percentage $5\%8\%10\%$

Hours per customer per monthly visit $5\mathrm{.}03\mathrm{.}02\mathrm{.}5$

a$.$ Develop a monthly plan that indicates the number of customers Maria should call on in each classification to maximize her monthly sales commissions.

b$.$ Determine the monthly commissions Maria will earn if she implements this plan.

In the first table, calculate the commission per customer and per hour for each customer classification.

In the second table, complete the monthly call$/$visit plan that would maximize Maria's monthly sales commissions. Then determine Maria's monthly commissions if she implements this plan.

Commission

per customer Commission

per hour

Large business Answer

$225$

Answer

$45$

Small business Answer

$192$

Answer

$64$

Individual Answer

$110$

Answer

$44$

Monthly Call$/$Visit Plan

Total number

of customers

Total number

of visit hours

Total

commissions

Large business Answer

$8$

Answer

$40$

Answer

$1,800$

Small business Answer

$35$

Answer

$105$

Answer

$6,720$

Individual Answer

$80$

Answer

$200$

Answer

$8,800$

Grand totals: Answer

$123$

Answer

$345$

Answer

$17,320$