1. A company manufactures a different manufacturing technique. Each Super Ball machine requires 25 hours of labor, 8 two kinds of pinball machines, each requiring hours of testing, and yields a profit of $350. Each Silver Ball machine requires 12.5 hours of labor, 8.5 hours of testing, and yields a profit of $200. There are 2500 hours of labor and 1200 hours of testing available.
The company has made contracts with the retailers to provide at least 60 Super Ball machines and at least 58 Silver Ball machines. The company wants to manufacture at most a combined total of 135 of Super Ball and Silver Ball machines.
How many of each kind of pinball machines the company should manufacture to maximize the total profit?
Formulate a linear programming model for the above situation by determining
(a) The decision variables.
(b) The objective function.
(c) All the constraints.
2. Charm City Foods manufactures a snack bar by blending two ingredients: a nut mix and a granola mix. Information about the two ingredients (per ounce) is shown below.
Ingredient | Cost In Dollars | Fat Grams | Protein Grams | Calories |
Nut Mix | 0.90 | 20 | 6.5 | 650 |
Granola Mix | 0.45 | 3 | 2.2 | 55 |
The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the snack bar. The blend should contain no more than 1200 calories, at least 12 grams of protein, and no more than 32 grams of fat. In addition, at least one ounce of nut mix must be included in the blend. The objective is to minimize the total cost.
Formulate a linear programming model for the above situation by determining
(a) The decision variables.
(b) The objective function.
(c) All the constraints.
