Exam 3: Linear Programming: a Geometric Approach

Find the graphical solution of the inequality. ​ 5x - 10 < 0 ​

Write a system of linear inequalities that describes the shaded region. ​

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​

Write a system of linear inequalities that describes the shaded region.

Determine graphically the solution set for the following system of inequalities.

Formulate but do not solve the following exercise as a linear programming problem. A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. He has decided that the meals should contain a minimum of 400 mg of calcium, 9 mg of iron, and 35 mg of vitamin C. He has further decided that the meals are to be prepared from foods A and B. Each ounce of food A contains 35 mg of calcium, 1 mg of iron, 3 mg of vitamin C, and 3 mg of cholesterol. Each ounce of food B contains 25 mg of calcium, 0.6 mg of iron, 7 mg of vitamin C, and 7 mg of cholesterol. Find how many ounces of each type of food should be used in a meal so that the cholesterol content is minimized and the minimum requirements of calcium, iron, and vitamin C are met.

Solve the linear programming problem by the method of corners. Minimize subject to

D11etermine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​

Write a system of linear inequalities that describes the shaded region.

A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3,300 labor-hours available. If he expects to make a profit of $100/acre on crop A and $140/acre on crop B, how many acres of each crop should he plant in order to maximize his profit? ​ __________ acres of crop A, __________ acres of crop B ​ What is the optimal profit? $ __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; C = __________

Write a system of linear inequalities that describes the shaded region. ​

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​

Determine graphically the solution set for the system of inequalities.

Find the graphical solution of the inequality. ​ ​

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​

Patricia has at most $36,000 to invest in securities in the form of corporate stocks. She has narrowed her choices to two groups of stocks: growth stocks that she assumes will yield a 13% return (dividends and capital appreciation) within a year and speculative stocks that she assumes will yield a 26% return (mainly in capital appreciation) within a year. Determine how much she should invest in each group of stocks in order to maximize the return on her investments within a year if she has decided to invest at least 3 times as much in growth stocks as in speculative stocks. $__________ in growth stocks and $ __________ in speculative stocks maximum return: $ __________

Find the graphical solution of the inequality. ​ ​

You are given a linear programming problem. Find the shadow price for resource 1. Maximize P = 5x + 4y

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.