1/Solve the following linear programming problem.

Maximize:Z=8x+18y

subjectto

6x+7y42

12x+y42

x0, y0

The maximum value is...

The maximum occurs at the point...

2/Use graphical methods to solve the following linear programming problem.

Maximize:

z=5x+y

subjectto:

xy5

5x+3y75

x0, y0

Graph the feasible region using the graphing tool to the right.

The maximum value of z is..., at the corner point....

3/Find the minimum and maximum values of

z=5x+3y

(if possible) for the following set of constraints.

3x+y30

15x+y54

3x+5y54

Select the correct choice belowand, ifnecessary, fill in the answer box to complete the choice.

A.The minimum value is....

B.There is no minimum value.

Select the correct choice belowand, ifnecessary, fill in the answer box to complete the choice.

A.The maximum value is....

B.There is no maximum value.

4/Write the constraint below as a linear inequality.

A canoe requires4hours of fabrication and a rowboat5hours. The fabrication department has at least81hours of labor available each week. Let x be the number of canoes and let y be the number of rowboats.

Choose the inequality that represents the given constraint.

A.5x+4y81

B.4x+5y81

C.4x+5y81

D.5x + 4y81

5/Deluxe coffee is to be mixed with regular coffee to make at least 53 pounds of a blended coffee. The mixture must contain at least15pounds of deluxe coffee. Deluxe coffee costs $4 per pound and regular coffee $3per pound. How many pounds of each kind of coffee should be used to minimizecosts?

To attain the minimumcost, use...pounds of deluxe coffee and...pounds of regular coffee.

6/Kevin is an auto mechanic. He spends2hours when he replaces the shocks on a car and2hours when he replaces the brakes. He works no more than54hours a week. He routinely completes at least 4shocks replacements and6brake replacements a week. If he charges $400 for labor replacing shocks and $250in labor for replacingbrakes, how many jobs of each type should he complete a week to maximize hisincome?

Kevin should do...shock replacements and...brake replacements every week to maximize his weekly income.