Quantitive Methods of Business – Extra Credit Assignment

Quantitive Methods of Business (Statistics) – Extra Credit Assignment

Subject: Mathematics    / Statistics
Question
Section 8.1 Expanded: Constructing the nonlinear profit contribution expression
Let PS and PD represent the prices charged for each standard golf bag and deluxe golf bag respectively. Assume that “S”
and “D” are demands for standard and deluxe bags respectively.
S = 2250 – 15PS
D = 1500 – 5PD (8.1)
(8.2) Revenue generated from the sale of S number of standard bags is P S*S. Cost per unit production is $70 and the cost for
producing S number of standard bags is 70*S.
So the profit for producing and selling S number of standard bags = revenue – cost = P SS – 70S
(8.3)
By rearranging 8.1 we get
15PS = 2250 – S or
PS = 2250/15 – S/15 or
PS = 150 – S/15 (8.3a) Substituting the value of PS from 8.3a in 8.3 we get the profit contribution of the standard bag:
(150 –S/15)S – 70S = 150S – S2/15 – 70S = 80S – S2/15 (8.4) Revenue generated from the sale of D number of deluxe bags is P D*D. Cost per unit production is $150 and the cost for
producing D number of deluxe bags is 150*D.
So the profit for producing and selling D number of deluxe bags = revenue – cost = P DD – 150D
(8.4a)
By rearranging 8.2 we get
5PD = 1500 – D or
PD = 1500/5 – D/5 or
PD = 300 – D/5 (8.4b) Substituting the value of PD from 8.4b in 8.4a we get the profit contribution of the deluxe bags:
(300 -D/5)D – 150D = 300D – D2/5 – 150D = 150D – D2/5 (8.4c) By adding 8.4 and 8.4c we get the total profit contribution for selling S standard bags and D deluxe bags.
Total profit contribution = 80S –S2/15 + 150D – D2/5
(8.5)
Homework assignment:
Reconstruct new objective function for 8.5 by changing “15P S” to “8PS” in 8.1, “5PD” to “10PD” in 8.2, cost per unit
standard bag from 70 to “last two digits of your UTEP student ID” and cost per unit deluxe bag from 150 to 125. Use up
to 2 decimal points accuracy.
Substitute the new expression for 8.5 in the excel solver workbook explained in the class and solve for the optimal
combination values for S and D. Submit the printout from the excel solution in March 9, 2017 class. Instructor will not
accept any late homework. Make sure you submit the results (just one page excel printout). Write your full name in
upper case, last 4 of your UTEP student ID, and, the new objective function expression (like equation 8.5 above) on the
printout. If you fail to follow the instructions you will lose points.