g locations for a given product and six major markets. Each manufacturing center
ID: 3727244 • Letter: G
Question
g locations for a given product and six major markets. Each manufacturing center has different costs, and each market has different prices for the product. In addition the distances between manufacturing locations and markets varies and so does the transportation cost. The company has calculated the net profit, cy, of producing the good at location i and selling it in market j. These net profit figures, together with the maximum manufacturing capability at each location and demand at each market are shown in the table below. Markets 1 29 51 59 54 56 27 2 44 43 29 63 53 46 1200 Plants 1800 3 63 37 63 62 46 47 1100 37 29 53 63 63 S1 4 51 53 54 51 43 38 1000 1200 700 1500 500 1100 1900 (a) What is the optimal way for the company to produce and sell its product? [Hint: Remember that the company is a profit maximizer.] (b) What is the interpretation of the dual variables? (c) Which plant (if any) would you recommend expanding? (d) Which plant (if any) would you recommend reducing in size? (e) Which sales territory is the most profitable? (f) Which sales territory is the least profitable? Please solve by using GAMS software and in addition if it is possible load solve summary of problem with Ist. fileExplanation / Answer
a. The optimum way for the organisation is to increase the product manufacturing to max for those plants to be distributed among the market where profit margin is more first and then allocate the remaining capacity to other market areas. Keep on doing this for all market spaces for maximum profit.
b. Dual variable indexing is just a two dimentional way of representing data in order to gie it a relational representation. Fo example - Here above in the table itself, we have net profit provided for each plant for a perticular market. We write it as - Net profit [Plant_Name] [Market Name]
c, Plant 4 as it is having best profit margit for all the market types as an whole with respect to all other plants.
d. Plant 1 as it is having least profit margit for all the market types as an whole with respect to all other plants.
e. Territory 4 is the mest profitable as it has best profit margin for all the plants.
f.Territory 5 is least profitable as it has very less demand even though have reasonable profit margin.
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