Exam 8: Linear Programming

Use the simplex method to maximize Z = 2 - 3 subject to + ≥ 5 + 2 ≤ 8 , ≥ 0

Sketch the region described by the following system of inequalities:

Use the simplex method to minimize Z = 3 + 2 Subject to , ≥ 0

Sketch the region described by the inequalities.

A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost.The average monthly salary of a counselor is $2400 and the average 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 may have up to 3 aides for every 2 counselors.How many counselors and how many aides should the camp hire to minimize cost?

Sketch the region described by the inequalities

Use the dual and the simplex method to minimize Z = 4 + 5 subject to - ≥ 4 2 - ≥ 1 5 + 3 ≥ 3 , ≥ 0.

The region indicated in the diagram is described by

A manufacturer produces two products,product A and product B.Both products require processing on Machines I and II.The number of hours needed to produce one unit is given by the following chart: Machine I is available for at most 1000 hours and Machine II is available for at most 2500 hours.If the profit made on product A is $20 / unit and the profit made on product B is $25 / unit.Find the production level that will maximize profit and find the Maximum profit.

In the initial simplex table below,find the departing variable.

A person decides to take two different dietary supplements.Each supplement contains two essential ingredients,A and B,for which there are minimum daily requirements,and each contains a third ingredient,C,which needs to be minimized.Find the amount of each supplement that the person should take each day in order to satisfy the requirements for A and B while minimizing C.Also find the amount of C the person takes each day.

2x - 3y ≥ 6

Maximize Z = - 2 + 3 Subject to

Maximize Z = 2x - 3y subject to 2x + y ≥ 1 x - y ≤ 1 x,y ≥ 0. Also find the corner point where the value of z is attained.

Find the dual problem to the following: The What If Company has $30,000 for the purchase of material to make three types of gadgets.The company has allocated a total of 1200 hours of assembly time and 180 hours of packaging time for the gadgets.The following table gives the cost per gadget,the number of hours per gadget,and the profit per gadget for each type. What is the number of gadgets of each type the company should produce to maximize profit?

When no quotients exist in a simplex table,

Maximize Z = 4x + 6y subject to

The region indicated in the diagram is described by

Use the simplex method to maximize Z = + 4 + subject to .

A company manufactures two models of inline skates,Alpha and Beta,at two different manufacturing plants.The maximum output at plant I is 1000 per month,while the maximum output at plant II is 1200 per month.Due to contractual obligations,the number of Alpha models produced at plant I must exceed the number of Beta models produced at plant I by at least 100.The profit per Alpha and Beta model manufactured at plant I is $50 and $80,respectively,while the profit per Alpha and Beta model manufactured at plant II is $60 and $70,respectively.This month,the company received an order for 900 Alpha and 1000 Beta models.Find how many of each model should be produced at each plant in order to satisfy the order and maximize the profit.(Hint: Let represent the number of Alpha models and represent the number of Beta models manufactured at plant I.)