Question #1

Graph the solution set of the inequality.

4x + 5y > 80

Question #2

Form the dual maximization problem (Usex₁andx₂as the variables andfas the function.) and use the simplex method to solve the minimization problem. Assume that all variables are nonnegative.

Minimize g=3y₁+2y₂,

subject to the following.

5y1+2y216

3y1+7y227

Maximizef= ---------------------subject to

-------------- 3 --------------2

x1, x20

The minimum value of the objective function is_________which occurs at

(y₁,y₂) = ---------------

Question #3

Form the dual maximization problem (Usex₁,x₂, andx₃as the variables andfas the function.) and use the simplex method to solve the minimization problem. Assume that all variables are nonnegative.

Minimize g=15y₁+14y₂,

subject to the following.

y1+y2100

2y1+y2140

6y1+5y2580

Maximizef= ------------- subject to ------------15

------------14

x1, x2, x30

The minimum value of the objective function is----------- which occurs at

(y₁,y₂) = ----------

.

.