Lesson 3.8: Linear Programming Answers

The constraints of a problem are graphed below. What are the vertices of the feasible region?

The constraints of a problem are listed below. What are the vertices of the feasible region?

A chicken farm orders bags of feed from two stores. Store X charges $20 per bag, and store Y charges $15 per bag. The farm must obtain at least 60 bags per week to care for the chickens properly. Store Y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store X as from store Y. The chicken farm wants to minimize the cost of ordering feed. Let x represent the number of bags of feed from store X and y represent the number of bags of feed from store Y. What are the constraints for the problem?

A botanist is using two types of plants for an experiment. She writes inequalities to model the constraints on the number of each type of plant she can use. She uses linear programming to find the vertex of the feasible region that results in the minimum value, in dollars, of the cost function. If that vertex is (5, 39), what do the coordinates represent?

Which ordered pair maximizes the objective function P = 3x + 8y?

What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below?

The constraints of a problem are listed below. What are the vertices of the feasible region?

A catering business offers two sizes of baked ziti. Its small ziti dish uses 1 cup of sauce and cups of cheese. Its large ziti dish uses 2 cups of sauce and 3 cups of cheese. The business has 100 cups of sauce and 400 cups of cheese on hand. It makes $6 profit on their small dishes and $5 profit on their large dishes. It wants to maximize the profit from selling the two sizes of ziti. Let x represent the number of small dishes and y represent the number of large dishes. What are the constraints for the problem?

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for $8, and nonflowering plants sell for $5. Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants. What are the vertices of the feasible region for this problem?

Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses cup of oil and 2 eggs. For a tray of bran muffins, Alan uses cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of trays of blueberry muffins and y represent the number of trays of bran muffins Alan bakes. What are the constraints for the problem?