Question

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	8	35	80
Average monthly sales per customer	$2,500	$1,500	$600
Commission percentage	5%	8%	10%
Hours per customer per monthly visit	5.0	3.0	2.5

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??	Answer??
Small business	Answer??	Answer??
Individual	Answer??	Answer??

	Monthly Call/Visit Plan
	Total number of customers	Total number of visit hours	Total commissions
Large business	Answer??	Answer??	Answer??
Small business	Answer??	Answer??	Answer??
Individual	Answer??	Answer??	Answer??
Grand totals:	Answer??	Answer??	Answer??

Answer 1

Solution :- Maria paiet working about 80 hrs per week Calling Customers each month. On a total of 123 yegulay Large business : Commission per customer = Average montly Sales pey Customer Commission percentage : = => $2,500* 54. 125 . Commission per hour >> Commission per customer number of hours per cos tomei on monthly basis 125.5.0: 25 Commission Per costomer Commission Per hour 125 25 Lorge business Small business 120 ho individual 24

Small business Commission per customer = 1,500*87. = 120 Commission per houx = 180/3.0 40 Individual Commission per customer = 600*102.. 60 Commission per hour := 60/2.560 - 24 * family & health considerations, she has decided to reduce her hours. * As hours is a constraint & objective is to maximize Commission here, we would devise monthly pion on the basis of Commission per hour * As Commission per hour is maximum for small business. need to first accommodate hours to visit Smau bussiness. Coustomers.

If 35 small business Costomers are visited then left out hours are :) 160-(35*3) .. » 55 Now, we need to maximize the 55 Yest of hours :-) win first tyy to allocate Large bossiness Costomers. large bussiness Costomers the " Aftey allocating an of the 0. . left out hours 55-40 15 Ieft 006 hours would would be allocated to individual business hours * 9.5 => 15 6 customers can only be visited : - Total number of visit hours No. of customers to visit * hovis per visit Total Commission Total no.o visit hours Commission per hy

' Monthly Cau/visit plan To tal no-of | Total no. of I Total Customers visit hours Cos tomers H0 2200 Large business 105 7560 Small business 780 individual Crond total : .: 160 rosuo In the above table, Shows Complete the monthly Can I visit pian that would maximize maria's monthly Saies Commissions the Commission Obiective is to maximize Commission from Saie per Large bussiness. Customer - $ 2,500 * 54 $2,500 *0.05 Commission from Sale per large bussiness Customer V $1,500*81. = $ 1,500 0.08 Commission from Sale per lorge business Customer = $.600*107. = $ 6000-

objective tonction .MAX No. of Costomers from each category X1 = 8 X2 <= 35 79<80 where . Xi - NO.of large business Costomers to visit X2 = No of Smau business Costomers to visit X = No.of individual bussiness Customers to visit No of hours available to work ( 5xl +3x2 +8.5x9 = 160 the 10.04 Costomers magia that indicates Monthly plan to maximize her Should can on in each classification monthly Sales Commissions. X = 8 X2 - 35 X3 = 6 Maximum Commission = 10540