Exam 5: Linear Inequalities and Linear Programming

Use graphical methods to solve the linear programming problem: -

Graph the inequality: -y < - 2

The corner points for the bounded feasible region determined by the system of inequalities: are O = (0, 0), A = (0, 7), B = (6, 5) and C = (8, 0). Find the optimal solution for the objective profit function:

Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or unbounded: -

Formulate the following problem as a linear programming problem (DO NOT SOLVE):A small accounting firm prepares tax returns for two types of customers: individuals and small businesses. Data is collected during an interview. A computer system is used to produce the tax return. It takes 2.5 hours to enter data into the computer for an individual tax return and 3 hours to enter data for a small business tax return. There is a maximum of 40 hours per week for data entry. It takes 20 minutes for the computer to process an individual tax return and 30 minutes to process a small business tax return. The computer is available for a maximum of 900 minutes per week. The accounting firm makes a profit of $125 on each individual tax return processed and a profit of $210 on each small business tax return processed. How many of each type of tax return should the firm schedule each week in order to maximize its profit? (Let equal the number of individual tax returns and the number of small business tax returns.) Graph the constant-profit lines through (3, 2) and (5, 3). Use a straightedge to identify the corner point(s) where the maximum profit occurs for the given objective function.

The corner points for the bounded feasible region determined by the system of inequalities: are O = (0, 0), A = (0, 4), B = (5, 2) and C = (7, 0). Find the optimal solution for the objective profit function:

Formulate the following problem as a linear programming problem (DO NOT SOLVE):A dietitian can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.02. Each ounce of chicken contains 13 units of protein and 24 units of carbohydrates. Each ounce of potatoes contains 5 units of protein and 35 units of carbohydrates. The minimum daily requirements for the patients under the dietitian's care are 45 units of protein and 58 units of carbohydrates. How many ounces of each type of food should the dietitian purchase for each patient so as to minimize costs and at the same time insure the minimum daily requirements of protein and carbohydrates? (Let equal the number of ounces of chicken and the number of ounces of potatoes purchased per patient.)

Graph the inequality: -2x + y $\le$ 1

Use graphical methods to solve the linear programming problem: -

Graph the inequality: -4x - 2y $\le$ 8

Solve the following linear programming problem by determining the feasible region on the graph below and testing the corner points:

Use graphical methods to solve the linear programming problem: -

Graph the inequality: -x + 5y $\ge$ 2

Find the coordinates of the corner points of the solution region for:

Using a graphing calculator as needed, Give the answer to two decimal places.

Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or unbounded: -

The Old-World Class Ring Company designs and sells two types of rings: the BRASS and the GOLD. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one BRASS ring and 2 man-hours to make one GOLD ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a BRASS ring is $40 and on an GOLD ring is $30?

Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or unbounded: -

Using a graphing calculator as needed, Give the answer to two decimal places.

Refer to the following system of linear inequalities associated with a linear programming problem: (A) Determine the number of slack variable that must be introduced to form a system of problem constraint equations. (B) Determine the number of basic variables associated with this system.