- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 1 (55.1 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 2 (34.53 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 3 (81.72 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 4 (20.85 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 5 (20.85 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 6 (43.21 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 7 (79.42 KiB) Viewed 23 times
- Prblem Description A Company Produces 10 Products In 7 Different Variations Of Each Product There Are Three Scarce Res 8 (67.3 KiB) Viewed 23 times
100 The unit costs for the resources differ from one resource to another, where these costs are estimated to be 84, 57 and 55 for resources 1, 2 and 3, respectively. Also, there is limited availability of the three resources, where 33000 units are available from resource I, 41000 from resource 2 and 45000 units from resource 3. The company is seeking to determine the monthly product Variation mix that maximizes the prodit. After surveying the market and taking into account the existence of other competitors who produce similar products, the company anticipates that its monthly sales of the respective products from all variations) won't exceed a Maximum amount as shown in the following table Table 3. Maximum sales for each product (units) Product P1 P2 P3 P4 PSP7 P89. PIO Max Sales 450 810 740 660 420 530 380 510 670 790 In addition, there are blending" constraints, where the percentage of variations 5 to 7 for any product can't exceed a certain percentage from the total amount produced from that product, and also can't be less than a minimum percentage, as shown in the following table Table 6. Maximum percentages of variations 5 to 7 allowed for each product Product 11 P2 13 14 PS PO P8 19 PRO Max MO 60 20 60 40 30 50 80 50 Min 20 1525 70 20 10 25 5 10 30 ?יו You have been hired by the company to assist then in solving the product mix problema hand. Cooduet the necessary analysis and provide the management with a report that provides thorough answers to the following question
k) Comment on the utilization of the resources available in this problem (i.e., which of the resources have been fully utilized and which haven't). 1) What is the maximum amount that the company should be willing to pay in order to increase the available amount of cach of the resources, one at a time, by one unit (assuming that such an increase is possible)? m) Assuming the company could acquire more units of a particular resource, which resource should the company acquire more of, and how much more of that resource should be acquired? n) If the monthly availability of resource 1 is increased from the current 33000 units to 38000 units, is the shadow price associated with that constraint still valid to assess what impact this increase in the right hand side would have on the objective function value? Why or why not? o) Assume that due to unforeseen circumstances, the availability of resource 3 drops from 45000 to 40000. How would such unexpected drop impact the company's production policy? P) Assess the impact of changing the following selling prices, one at a time, on the current optimal solution, by just indicating whether the current optimal solution remains optimal or not, and why: 1) Increasing the selling price of PS-V4 from S126 to $135. 2) Reducing the selling price of P8-V3 from $100 to $90. 3) Increasing the selling price of P10-v5 from $93 to $105. 2) If the company could sell as much as it produces from one particular product (i.e. no maximum files restriction), which product would that be, and why? (show detailed analysis) 1) Now, as pati of a marketing campaign, let us say that the company is considering reducing the selling price of all variations from a particular product by 20%, and the anticipated effect would be an increase in the maximum sales of that specific product by 30%. Which product should the company go ahead and reduce its price and why? (show detailed analysis) 3) If a new competitor enters the market, which would reduce the maximum sales of all products equivalently by 15%, what would be the contingent optimal production strategy in this case, and what is the impact on the company's total profit?
Now assume the opposite scenario where a major competitor closes down resulting in an increase of 15% in the maximum sales of all products. To cope with such an increase in the demand, the company has the option to acquire up to 10000 units more of each of the three resources (if deemed necessary) at an extra cost of Si per additional unit of any resource (.e. $5,88 and 56 per additional unit of resources 1, 2 and 3, respectively). This is the case since those additional units are obtained on an expedited basis, and are thus more expensive (i.c., outsourcing, overtime, etc.). Determine the revised production policy and how much of the possible extra 10000 units of each resource were utilized (if any)? interpretation. k) Comment on the utilization of the resources available in this problem (i.e., which of the resources have been fully utilized and which haven't). 1) What is the maximum amount that the company should be willing to pay in order to increase the available amount of each of the resources, one at a time, by one unit (assuming that such an increase is possible)?
PRBLEM DESCRIPTION: A company produces 10 products in 7 different variations of each product. There are three scarce resources that are used to varying degrees to make these product variations, where the resource requirements per unit of the different products variations are shown in the following tables. Table 1. Consumption of resource 1 per unit of product variations Product Variation P1 P2 P3 P4 P5 P6 P7 P8 P9 PIO VI 7 6 4 6 | 8 5 2 2 3 7 V2 7 6 7 9 9 8 2 3 7 V3 7 8 7 9 9 8 2 3 8 V4 13 10 10 11 13 9 7. 4 11 V5 13 | 13 | 10 | 1113 9 7 9 4 11 V6 1313 10 | 11 13 9 4 11 V7 12 10 10 11 11 8 7 4 8 00 ها انو ته اتيا - CO DOO 0000 Sala NNN obowNN mm TTT
Table 2. Consumption of resource 2 per unit of product Variations Variation Product P1 P2 P3 P4 PS P6 P7 P8 P9 PIO V1 3 3 5 6 6 3 4 4 5 4 V2 3 3 56 6 3 4 7 4 V3 3 3 56 6 3 4 7 4 V4 4 S 6 8 6 3 4 7 4 V5 7 11 10 8 93 4 8 7 V6 8 12 13 9 93 4 8 6 7 V7 8 12 | 13 12 9 35 86 8 4 aauuuu oooc NNE ooooo Table 3. Consumption of resource 3 per unit of product variations Variation Product P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Vi 3 2 7 5 4 5 2 3 76 V2 3 2 7 9 6 V3 3 2 7 6 9 | 6 V4 3 5 75 6 9 6 V5 3 7 6 8 129 8 V6 5 7 11 9 5 10 12 9 8 V7 5 7 11 6 9 5 10 12 9 8 = = = = = = = UN alo annoo lululululululule |vlv|2|2| Sama 99 فما فما | الي 9 In addition, there are selling prices for all variations, which differ from one variation to another as shown in the following table. V2 Table 4. Selling prices of product Variations (S/unit) Product Variation P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Vi 71 57 94 103 102 72 50 58 95 88 71 56 109 105 115 84 56 101 103 91 V3 63 65 99 108 129 82 55 100 94 99 V4 77 97 113 143 126 75 57 101 98 88 VS 82 106 139 150 159 85 80 117 10493 V6 102 148 142 150 157 85 106 143 100 94 V7 111 165 150 171 180 86 119 154 110 100
In addition, there are selling prices for all variations, which differ from one variation to another as shown in the following table. Table 4. Selling prices of product variations (S/unit) Product Variation P1 P2 P3 P4 PS P6 P7 PS P9 P10 VI 71 57 94 103 10272 SO 58 95 88 V2 71 S6 109 105 11584 56 101 103 91 V3 63 65 99 108 129 82 55 100 94 99 V4 77 97 113143 126 75 57 101 98 88 VS 82 106 139 150 159 85 80 117104 93 V6 102 148 142 150 157 85 106 143 100 94 V7 111 | 165 150 171 180 86 119 154 110 100 SINE | - 818 ES The unit costs for the resources differ from one resource to another, where these costs are estimated to be $4, S7 and 5 for resources 1, 2 and 3, respectively. Also, there is limited availability of the three resources, where 33000 units are available from resource 1, 41000 from resource 2, and 45000 units from resource 3. The company is seeking to determine the monthly product/variation mix that maximizes the profit. After surveying the market and taking into account the existence of other competitors who produce similar products, the company PS anticipates that its monthly sales of the respective products (from all variations) won't exceed a maximum amount as shown in the following table. Table 5. Maximum sales for each product (units) Product P1 P2 P3 P4 P5 P6 P7 P9 P10 Max Sales 450 810 740 660 420 530 380 540 670 790 In addition, there are "blending" constraints, where the percentage of variations 5 to 7 for any product can't exceed a certain percentage from the total amount produced from that product, and also can't be less than a minimum percentage, as shown in the following table. Table 6. Maximum percentages of variations 5 to 7 allowed for each product Product P2 P4 P5 P6 P7 P8 P9 P10 Max % 80 70 60 140 80 50 80 50 Min % 20 15 25 20 tel:80%2060%2070%2060%2040%2080%2050 You have been hired by the company to assist then in solving the product mix problem at hand. Conduct the necessary analysis and provide the management with a report that provides thorough answers to the following questions, P1 P3 70 60