Set up and solve this word problem:

A cat breeder has 90 ounces (oz) of tuna, 80 ounces of liver, and 50 ounces of chicken.

A Siamese cat requires 2 oz of tuna, 1 oz of liver, and 1 oz of chicken per day.

A Persian catrequires 1 oz of tuna, 2 oz of liver, and 1 oz of chicken per day.

A Siamese cat sells for $12 while a Persian cat sells for $10.

How many of each kind of cat should be raised in order to maximize revenue?

You must define your variables x and y (write them down! - e.g. "Let x = number of Siamese cats"), write the objective function and the constraints, and set up the initial simplex tableau.Then solve the linear programming problem by the simplex method and write conclusion in the form of a sentence, specifying the maximum value of the objective function and the values of the variables that maximize it.Your answer should contain words such as revenue, Siamese cats, and Persian cats!

Use the graphical method to solve this minimization problem:

Minimize:

subject to:

Sketch a graph of the region bounded by these inequalities, shade the region, and label all four corner points on the graph.Evaluate the objective function at each of the four corners and show these values.Write you conclusion as a sentence specifying the the minimum value of the objective function and the values of x and y that minimize it.

Use the simplex method to solve this maximization problem:

Maximize:

subject to:

Write the constraints as equations with slack variables.Write them down!Write the initial simplex tableau.Select the pivot column and pivot row, then pivot.Repeat this process as often as necessary.Write conclusion as a sentence stating the maximum value of the objective function and the values of the variablesandthat maximize it.

Use the method of duals to solve this minimization problem:

Minimize:

subject to:

Write the augmented matrix whose first two rows are the first two constraints and whose 3rd row is the objective function.Transpose this matrix and state the dual maximization problem:"Maximize z = _____ subject to: _____".Write it down!Then proceed as in the previous problem.Write conclusion as a sentence, giving the minimum value of the objective function and the values of the variablesandthat minimize it.

Use the two-stage method to solve this nonstandard maximization problem:

Maximize:

subject to:

Stage I:Write the constraints as equations with either added slack variables (for ) or subtracted surplus variables (for ).Write these equations!Write the initial simplex tableau.Find a basic feasible solution, in which all basic variables are positive.Indicate where Stage I ends.

Stage II:Apply the usual simplex method to the tableau that ended Stage I.Write conclusion as a sentence, giving the maximum value of the objective function and the values of the variablesandthat maximize it.

Given the following initial simplex tableau:

(a)What is the problem that is being solved?Specify the objective function, whether it is to be maximized or minimized, and all five constraints.

(b)If the 1 in row 2, column 5 were changed to a , what would change in your answer to part (a)?

(c)After several steps of the simplex method, the tableau becomes:

What is the solution to the linear programming problem?In a sentence, write the maximum value of the objective function and the values of the original variables that maximize it.Don't include any slack or surplus variables.

Label the parts of your answer (a), (b), and (c).