Linear Programming — Cumulative exam Answers

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

Luis is saving money to purchase a new video game. He has a total of 30 coins consisting of nickels and dimes. The value of the coins is $2.20. Let n represent the number of nickels and let d represent the number of dimes. Which system of equations can be used to determine the number of nickels and the number of dimes Luis has?

What are the steps to solving the inequality < –2?

A store sells a certain tile for $2 per tile and a pint of paint for $3. A second store sells the same items for $1 per tile and $4 per pint of paint. Ari bought the same number of tiles and pints of paint at both stores, costing him $26 at the first store and $18 at the second store, before tax.

What is the solution to the inequality 28 > 4 – 2p?

Tiffany sells two kinds of homemade tomato sauce. A quart of her Tuscan sauce requires 6 tomatoes and 1 cup of oil. A quart of her marinara sauce requires 5 tomatoes and cups of oil. She makes $4 profit on each quart of her Tuscan sauce and $5 profit on each quart of her marinara sauce. She has 45 tomatoes and 10 cups of oil on hand. Tiffany wants to maximize her profits from selling the sauce.Let x represent the number of quarts of Tuscan sauce and y represent the number of quarts of marinara sauce Tiffany makes. What are the constraints for the problem?

A function g(x) is defined as shown.g(x) = What is the value of g(4)?

The graph represents the data cost for monthly Internet service for a cell phone.

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?

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

The sum of two numbers is 12. The first number, x, is twice the second number, y. Which system of equations could be used to find the two numbers?

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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 times and distances are represented by the function? Select three options.

The graph represents this system of equations:

Xavier can work no more than 40 hours in a week. He has already worked 24 hours this week. What is the maximum number of 8-hour days Xavier can work for the rest of the week?

Which functions represent a piece of the function? Select three options.

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

The graph represents this system of equations.

The cost in dollars to produce x cups of lemonade is represented by the function C(x)=10+0.20x. The revenue in dollars earned by selling x cups of lemonade is represented by the function R(x)=0.50x. What is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?