Question

Let P_Sand P_Drepresent 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 – 15P_S                                                                                                                                                                    (8.1)

D = 1500 – 5P_D                                                                                                                                                                      (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                                  

15P_S= 2250 – S or

                                    P_S= 2250/15 – S/15 or

                                    P_S= 150 – S/15                                                                                                                                                                     (8.3a)

Substituting the value of P_Sfrom 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                                  

5P_D= 1500 – D or

                                    P_D= 1500/5 – D/5 or

                                    P_D= 300 – D/5                                                                                                                                                                       (8.4b)

Substituting the value of P_Dfrom 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 “8P_S” in 8.1, “5P_D” to “10P_D” in 8.2, cost per unit standard bagfrom 70 to 91 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..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 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 in the formulation. If you fail to follow the instructions, you will lose points.

Answer 1