Exam 5: Integration

Provide an appropriate response. -Using a graphing calculator as needed, maximize P = 524x1 + 479x2 subject to 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. -

Give the mathematical formulation of the linear programming problem. Graph the feasible region described by the constraints and find the corner points. Do not attempt to solve. -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?

Give the mathematical formulation of the linear programming problem. Graph the feasible region described by the constraints and find the corner points. Do not attempt to solve. -Suppose an horse feed to be mixed from soybean meal and oats must contain at least 200 lb of protein and 40 lb of fat. Each sack of soybean meal costs $20 and contains 60 lb of protein and 10 lb of fat. Each sack of oats costs $10 and contains 20 lb of protein and 5 lb of fat. How many sacks of each should be used to satisfy the minimum requirements at minimum cost?

Provide an appropriate response. -Solve the following linear programming problem by determining the feasible region on the graph below and testing the corner points: x1 is shown on the x-axis and x2 on the y-axis.

Define the variable(s) and translate the sentence into an inequality. -Sales of wheat bread are at least $2000 greater than sales of white bread.

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

Use graphical methods to solve the linear programming problem. -

Graph the inequality. -

Solve the problem. -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?

Use graphical methods to solve the linear programming problem. -

Solve the problem. -A salesperson has two job offers. Company A offers a weekly salary of $180 plus commission of 6% of sales. Company B offers a weekly salary of $360 plus commission of 3% of sales. What is the amount of sales above Which Company A's offer is the better of the two?

Solve the problem. -Formulate the following problem as a linear programming problem (DO NOT SOLVE):A steel company produces two types of machine dies, part A and part B. Part A requires 6 hours of casting time and 4 hours of firing time. Part B requires 8 hours of casting time and 3 hours of firing time. The maximum number of hours per week available for casting and firing are 85 and 70, respectively. The company makes a $2.00 profit on each part A that it produces, and a $6.00 profit on each part B that it produces. How many of each type should the company produce each week in order to maximize its profit? (Let x1 equal the number of A parts and x2 equal the number of B parts produced each week.)

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 inequality. -

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

Provide an appropriate response. -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.

Provide an appropriate response. -Using a graphing calculator as needed, maximize P = 310x1 + 470x2 subject to Give the answer to two decimal places.

Define the variable(s) and translate the sentence into an inequality. -Enrollment is below 8000 students.

Solve the problem. -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 x1 equal the number of individual tax returns and x2 the number of small business tax returns.)