(Solved): 1. Using the 6 steps outlined, maximize the function P=14x+9y subject to the constraints: x+y93x ...

1. Using the 6 steps outlined, maximize the function $$P=14x+9y$$ subject to the constraints: $$\begin{array}{l}x+y?9\\ 3x+y?15\\ x?0\\ y?0\end{array}$$ Use the technique of linear programming to answer the following. 2. A company makes two products. Product $$\mathrm{A}$$ requires 3 hours of manufacturing and 1 hour of assembly. Produet B requires 4 hours of manufacturing and 2 hours of assembly. There are a total of 84 hours of manufacturing and 32 hours of assembly available. Using the 6 steps outlined to determine the production to maximize profit if the profit on product $$\mathrm{A}$$ is $$\$50$$ and the profit on product $$B$$ is $$\$60$$. 3. A diet is to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories. Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of vitamins, 30 units of minerals, and 10 calories. Fach unit of Food B provides 20 units of vitamins, 20 units of minerals, and 40 calories. If Food A costs $$\$2$$ per unit and Food B cost $$\$1$$ per unit, how many units of food should be purchased to keep costs at a minimum?