Section 8.1 Expanded: Constructing the nonlinear profitcontribution expression Let PSand PDrepresent the prices chargedfor each standard golf bag and deluxe golf bag respectively. Assumethat “S” and “D” are demands for standard and deluxe bagsrespectively. S = 2250 – 15PS (8.1) D = 1500 – 5PD (8.2) Revenuegenerated from the sale of S number of standard bags is PS*S. Costper unit production is $70 and the cost for producing S number ofstandard bags is 70*S. So the profit for producing and selling Snumber of standard bags = revenue – cost = PSS – 70S (8.3) Byrearranging 8.1 we get 15PS= 2250 – S or PS= 2250/15 – S/15 or PS=150 – S/15 (8.3a) Substituting the value of PSfrom 8.3a in 8.3 weget the profit contribution of the standard bag: (150 –S/15)S – 70S= 150S – S2/15 – 70S = 80S – S2/15 (8.4) Revenue generated from thesale of D number of deluxe bags is PD*D. Cost per unit productionis $150 and the cost for producing D number of deluxe bags is150*D. So the profit for producing and selling D number of deluxebags = revenue – cost = PDD – 150D (8.4a) By rearranging 8.2 we get5PD= 1500 – D or PD= 1500/5 – D/5 or PD= 300 – D/5 (8.4b)Substituting the value of PDfrom 8.4b in 8.4a we get the profitcontribution 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 totalprofit contribution for selling S standard bags and D deluxe bags.Total profit contribution = 80S –S2/15 + 150D – D2/5 (8.5)Reconstruct new objective function for 8.5 by changing “15PS” to“8PS” in 8.1, “5PD” to “10PD” in 8.2, cost per unit standardbagfrom 70 to “last two digits of your UTEP student ID” and costper unit deluxe bagfrom 150 to 125. Keep other parameter valuesunchanged. Use up to 2 decimal points accuracy. Substitute the newexpression for 8.5 in the excel solver workbook as explained in theclass and solve for the optimal combination values for S and D.Student ID last two numbers 52, I NEED THE EXAMPLE IN EXCEL SHEETFORMAT.
