Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. ( function is unbounded.) Maximize p = x + 2y subject to x + 6y ≤ 8 3x + y ≤ 7 x ≥ 0, y ≥ 0. p = Enter an exact number. (x, y) =

Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.

A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000

The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x energy drinks aremanufactured. (b) Find the revenue function R when x drinks are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the breakeven point means.