# Mr. Smith used the following information to calc

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