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ronald thump is interested in expanding his firm. after careful consideration, he has three areas in which he might invest additional funds...
ronald thump is interested in expanding his firm. after careful consideration, he has three areas in which he might invest additional funds determined: (1) product research and development, (2) manufacturing operations improvements, and (3) advertising and sales promotion. he has $ 500,000 available for investment in the firm. he can invest in its advertising and sales promotion program, every year, and each dollar invested in this manner is expected to yield a return of the amount invested plus 20% yearly. improvements in manufacturing operations he can invest every 2 years, with an expected return of the investment plus 30% (at the end of each 2-year period). an investment in product research and development would be for a 3-year period, with an expected return of the investment plus 50% (at the end of the 3-year period). to diversify the total initial investment, he wishes to include the requirement that at least $ 30,000 must be invested on the advertising and sales promotion programs, is at least $ 40,000 on manufacturing operations improvements, and at least $ 50,000 on product research and development initially (at the beginning of the first year). ronald wants to know how much should be invested in each of the three alternatives, during each year of a 4-year period, to maximize the total ending cash value of the initial $ 500,000 investment. a. formulate a linear programming model for this problem. b. solve this model by using the computer. Question 2: Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which has a 60% iron content; mine 3 produces pyrite ore, which has a 50% iron content; and mine 4 produces taconite ore, which has only a 30% iron content. Exeter has three customers that produce steel Armco, Best, and Corcom. Armco needs 400 tons of pure (100%) iron, Best requires 250 tons of pure iron, and Corcom requires 290 tons. It costs $37 to extract and process 1 ton of magnetite ore at mine 1, $46 to produce 1 ton of limonite ore at mine 2, $50 per ton of pyrite ore at mine 3, and $42 per ton of taconite ore at mine 4. Exeter can extract 350 tons of ore at mine 1; 530 tons at mine 2; 610 tons at mine 3; and 490 tons at mine 4. The company wants to know how much ore to produce at each mine in order to minimize cost and meet its customers' demand for pure (100%) iron.a. Formulate a linear programming model for this problem.b. Do any of the mines have slack capacity? If yes, which one(s)?c. If Exeter Mines could increase production capacity at any one of its mines, which should it be? Why?d. If Exeter were to decide to increase capacity at the mine identified in (b), how much could it increase capacity before the optimal solution point (i.e., the optimal set of variables) would change?e. If Exeter were to determine that it could increase production capacity at mine 1 from 350 tons to 500 tons, at an increase in production costs to $43 per ton, should it do so?
