Exam 5: Linear Inequalities and Linear Programming

Solve the problem. -Jim has gotten scores of 78 and 69 on his first two tests.What score must he get on his third test to keep an average of 70 or greater?

Use graphical methods to solve the linear programming problem. -Suppose an horse feed to be mixed from soybean meal and oats must contain at least 100 lb of protein,20 lb of fat,and 9 lb of mineral ash.Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein,10 lb of fat,and 8 lb of mineral ash.Each 100-lb sack of oats costs $10 and contains 20 lb of protein,5 lb of fat,and 1 lb of mineral ash.How many sacks of each should be used to satisfy the minimum requirements at minimum cost?

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. -P = x + y

Use graphical methods to solve the linear programming problem. -Maximize z = 8x + 12y subject to: 40x + 80y ≤ 560 6x + 8y ≤ 72 x ≥ 0 Y ≥ 0

Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or unbounded. -y ≤ -3x - 3 y ≥ x + 6

Provide an appropriate response. -Refer to the following system of linear inequalities associated with a linear programming problem: Maximize P = 3x₁ + 7x₂ subject to 5x₁ + x₂ ≤ 28 2x₁ + x₂ ≤ 13 x₁ + x₂ ≤ 0 x₁, x₂ ≥ 0 (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.

A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost.The monthly salary of a counselor is $2400 and the monthly salary of an aide is $1100.The camp can accommodate up to 45 staff members and needs at least 30 to run properly.They must have at least 10 aides,and at most twice as many aides as counselors.How many counselors and how many aides should the camp hire to minimize cost?

Solve the problem. -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 x₁ equal the number of ounces of chicken and x₂ the number of ounces of potatoes purchased per patient.)