Exam 4: Inequalities and Linear Programming

A farm co-op has over 6,000 acres available to plant with corn and soybeans. The farm co-op's maximum profit for planting 6,000 acres is $315,000 and the maximum profit for 6,008 acres is $315,320. What is the profit value of each additional acre of land? This value is called the shadow price of an acre of land. Round your answer to the nearest cent if necessary. ​

Solve the following linear programming problem. ​ Maximize subject to ​ ​

Solve the following linear programming problem. ​ Minimize subject to ​ ​

CDF Appliances has assembly plants in Atlanta and Fort Worth where they produce a variety of kitchen appliances, including a 12-cup coffee maker and a cappuccino machine. In each hour at the Atlanta plant, 160 of the 12-cup models and 200 of the cappuccino machines can be assembled and the hourly cost is $780. In each hour at the Fort Worth plant, 800 of the 12-cup models and 200 of the cappuccino machines can be assembled and the hourly cost is $2,120. CDF Appliances expects orders each week for at least 64,000 of the 12-cup models and at least 40,000 of the cappuccino machines. How many hours per week should each plant be operated in order to provide inventory for the orders at minimum cost? Find the minimum cost. ​

A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot. ​ ​

Use the simplex method to maximize the function (if possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, give one solution. ​ Maximize subject to ​ ​

Form the matrix associated with the given minimization problem and find its transpose. ​ Minimize subject to ​ ​

The graph of the boundary equations for the system of inequalities is shown with that system. Locate the solution region and find the corners. ​ ​ ​ ​

Use Excel or another technology to solve the following optimization problem. ​ Minimize subject to ​ ​

Solve the following linear programming problem. ​ Minimize subject to ​ ​

The graph of the boundary equations for the system of inequalities is shown with that system. Locate the solution region and find the corners. ​ ​ ​

State the given problem in a form from which the simplex matrix can be formed (that is, as a maximization problem with constraints). ​ Minimize subject to ​

A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched syrup. Suppliers can deliver at most 2,800 lb of wheat, at most 800 lb of sugar, and at least 1,000 lb of the vitamin-enriched syrup. If the profit is $0.80 on each pound of Senior Citizen's Feast and $1.00 on each pound of Kids Go, find the number of pounds of each cereal that should be produced to obtain maximum profit. Find the maximum profit. Round your profit to the nearest cent, another answers - to the nearest whole number. ​

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. ​ Maximize subject to ​ ​

Use the simplex method to maximize the given function. Assume all variables are nonnegative. ​ Maximize subject to ​ ​

The final simple matrix for a minimization problem is given below. Find the solution. ​ ​

Express the inequality as a constraint. ​

The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe drapes, 50 pairs of better drapes, and 6 pairs of standard drapes per day. The company has orders for 2,000 pairs of deluxe drapes, 4,200 pairs of better drapes, and 1,200 pairs of standard drapes. If the daily costs are $700 per day at location I and $800 per day at location II, how many days should Janie schedule at each location in order to fill the orders at minimum cost? Find the minimum cost. Round your answers to the nearest whole number if necessary. ​

A farm co-op has over 40,500 gallons of fertilizer/herbicide available to use when planting corn and soybeans. The farm co-op's maximum profit for using 40,500 gallons of fertilizer/herbicide is $315,009 and the maximum profit for 40,508 gallons is $315,034. What is the profit value of each additional gallon of fertilizer/herbicide (that is, the shadow price of a gallon of fertilizer/herbicide)? Round your answer to the nearest cent if necessary. ​

Graph the solution of the system of inequalities. ​ ​