Linear Programming Answers

Susan wants to make pumpkin bread and zucchini bread for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her recipe for one loaf of pumpkin bread uses 2 eggs and 3 cups of flour. Her recipe for one loaf of zucchini bread uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and zucchini bread loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes. What is the objective function for the problem?

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

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?

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?

A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month?

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

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

Lee washes the outsides of houses. It takes him 40 minutes to power wash a one-story home, and he uses 180 gallons of water. Power washing a two-story home takes 90 minutes and uses 300 gallons of water. Lee works no more than 40 hours each week, and he uses a maximum of 5,000 gallons of water per week. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his weekly washing income washing houses. Let x represent the number of one-story houses and y represent the number of two-story houses. 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?

Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats.When writing constraints for the problem, which definition for the variables x and y can be used to determine the maximum?

Which ordered pair minimizes the objective function C = 60x + 85y?

The vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). What is the maximum value of the objective function P if P = 180x + 250y?

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?

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?