Mr. Smith used the following information to calculate the profit coefficients for Aqua-Spas and Hydro-Luxes: pumps cost $225 each, labor costs $12 per hour, tubing costs $2 per foot. In addition to pumps, labor, and tubing, the production of Aqua-Spas and Hydro-Luxes consumes, respectively, $243 and $246 per unit in other resourses that are not in short supply. Using this information, Mr. Smith calculated the marginal profits of Aqua-Spas and Hydro-Luxes as: Aqua-Spas Hydro-Luxes Selling Price $950 $875 Pump Cost -$225 -$225 Labor Cost -$108 -$72 Tubing Cost -$24 -$32 Other Variable Costs -$243 -$246 Marginal Profit $350 $300 Howie’s accountant reviewed these calculations and thinks Howie made a mistake. For accounting purposes, factory overhead is assigned to products at a rate of $16 per labor hour. Howie’s accountant argues that because Aqua-Spas require nine labor hours, the profit margin on this product should be $144 less. Similarly, because Hydro-Luxes require six labor hours, the profit margin on this product should be $96 less. Who is right and why?2. Are the following objective functions for an LP model equivalent? That is, if they are both used, one at a time, to solve a problem with exactly the same constraints, will the optimal values of X1 and X2 be the same in both cases? Why or why not? MAX: 2X1 + 3X2 MIN: -2X1 – 3X2
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