Section 8.1 Expanded: Constructing the nonlinear profit contribution expression Let P S and P D represent the prices charged for each standard golf...

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                                                                                                                                               (8.1)

D = 1500 - 5PD                                                                                                                                                (8.2)

Revenue generated from the sale of S number of standard bags is PS*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 = PSS - 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 PD*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 = PDD - 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 "15PS" 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. Keep other parameter values unchanged. Use up to 2 decimal points accuracy. Substitute the new expression for 8.5 in the excel solver workbook as explained in the class and solve for the optimal combination values for S and D. Submit the printout from the excel solution in March 7, 2018 class. Instructor will not accept any homework late or submitted outside the class. Make sure you submit the results (just one page excel printout). Write/type your full name (first name first) in upper case, last 4 of your UTEP student ID, and, your new objective function expression (like equation 8.5 above) on the printout. Use S and D instead of b15 or c15. If you fail to follow the instructions, you will lose points.