In solving the following problems kindly show all your work in details. Answers (end results) with no details will not be corrected.

Graphically solve the following problem.

Maximize Profit = 8X1 + 5X2

Subject to:

X1 + X2 10

2X1 6

X1 , X2 0

1. What is the optimal solution?
2. Change the right hand side of constraint 1 to 11 (instead of 10) and resolve the problem. How much did the profit increase as a result of this?

Graphically solve the following problem, after identifying the Decision Variables, Objective Function and Constraints.

A clothing company makes short-sleeve and long-sleeve shirts. Each long-sleeve shirt nets

the company $4 in profit, and each short-sleeve shirt nets the company $3. Each shirt must be processed by two sewing machinesMachine I and Machine II.

Long-sleeve shirts require 3 minutes on Machine I and 1 minute on Machine II. Short-sleeve shirts require 2 minutes on each machine. Every day, Machine I is available for 10 hours and Machine II is available for 7 hours.

How many shirts of each type should the company produce each day so as to maximize profits?

Graphically solve the following problem.

Minimize the cost = X + 2 Y

Subject to: X+3Y >= 90

8X + 2Y >= 160

3X + 2Y >= 120

Y <= 70

X,Y >= 0

1. What is the optimal solution?
2. Change the right hand side of constraint 2 to 140 (instead of 160) and resolve the problem. What is the new optimal solution?