For Exercises 13-18,
a. For the given constraints, graph the feasible region and identify the vertices.
b. Determine the values of x and y that produce the maximum or minimum value of the objective function on the feasible region.
c. Determine the maximum or minimum value of the objective function on the feasible region.
Maximize:
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- Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.arrow_forwardA 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 12,000arrow_forwardThe graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. z = 5x + 8y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value is B. The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is B. The minimum value does not exist. 10+ Q N The coordinates of the corner points are (2,2), (3,8), (7,7), and (8,3).arrow_forward
- The graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. z=2x+4y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value is B. The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is B. The minimum value does not exist. 10- ON The coordinates of the corner points are (1,2), (3,9), (7,8), and (9,3).arrow_forwardThe graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. z = 7x+9y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value is B. The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is B. The minimum value does not exist. 10- Q 0 The coordinates of the corner points are (2,2), (3,9), (6,8), and (8,3).arrow_forwardThe graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. z = 5x + 4y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value is B. The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is B. The minimum value does not exist. My 10- X 0 10 The coordinates of the corner points are (1,2), (4,9), (7,7), and (9,4).arrow_forward
- The graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. z = 2x+8y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The maximum value is B. The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is B. The minimum value does not exist. 10- Q 10 The coordinates of the corner points are (1,1), (4,9), (8,8), and (9,4).arrow_forwardA paper manufacturing company converts wood pulp to writing paper and newsprint. The profit on a unit of writing paper is $500 and the profit on a unit of newsprint is $350. Solve, a. Let x represent the number of units of writing paper produced daily. Let y represent the number of units of newsprint produced daily. Write the objective function that models total daily profit. b. The manufacturer is bound by the following constraints: * Equipment in the factory allows for making at most 200 units of paper (writing paper and newsprint) in a day. * Regular customers require at least 10 units of writingpaper and at least 80 units of newsprint daily. Write a system of inequalities that models these constraints. c. Graph the inequalitiers in part (b) Use only the first quadrant, because x and y must both be positive. (Suggestion: Let each unit along the x- and y-axes represent 20.) d. Evaluate the objective function at each of the three vertices of the graphed region. e. Complete the missing…arrow_forward
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