Linear Programming — Cumulative exam Answers

Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.

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

The piecewise function f(x) has opposite expressions.f(x) = Which is the graph of f(x)?

Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?

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?

The function g(x) is defined as shown.

What is the solution to the inequality + 4 ≤ 0?

Tamara is creating a model of a rectangle. She has 26 inches of yellow ribbon to use for the border of the rectangle. She wants the length, l, to be 3 inches greater than the width, w. Which system of equations could Tamara use to find the dimensions of a rectangle that uses all of the ribbon?

The product of two numbers is 32. The first number, x, is one-half of the second number, y.

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

The piecewise function h(x) is shown on the graph.

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?

Mrs. Valdez wanted to determine the number of people, p, she could safely take in her car to the fun run. She determined that p < 5.

What is the best first step to solve the inequality 5x – 3 ≥ 2?

Paul is comparing two high-speed Internet service providers (ISPs) for his business. The graph represents the cost of each ISP as a function of t, the duration in months of a service contract.

Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30?

A piecewise function f(x) is defined as shown.f(x) = Which table could be used to graph a piece of the function?

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

The function h(x) is defined as shown.h(x) =

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?