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Hawkins manufacturing Company produces connection rods for 4- and 6- cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2000, and the cost required to set up the production line for the 6- cylinder connecting rods is $3500. Manufacturing costs are $15 for each 4- cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If there is a production changeover from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let
= the number of 4-cylinder connecting rods produced next week
= the number of 6-cylinder connecting rods produced next week
= 1 if the production line is set up to produce the 4-cylinder connecting
rods 0 otherwise
= 1 if the production line is set up to produce the 6-cylinder connecting
rods 0 otherwise
a. Using the decision variables and write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8000 units
b. Using the dicision variables and , write a constraint that limest next weeks production of the 6-cylinder connectiong rods to either 0 or 8000 units.
c. Write three constraints that, taken together, limit the production of connecting rods for next week.
d. Write an objective function for minimizing the cost of production for next week.
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Is integer values a general property of LinearProgramming problems? Explain why rounding or truncating non-integer values for the solutions is not an appropriate method for obtaining integer solutions.

You are trying to determine the best mix of bombers, fighters, and refueling aircraft in the next generation of the Air Force budget. You want to optimize effectiveness, subject to a variety of constraints, including cost. You plan to use linearprogramming, but know that you cannot have a portion of an aircraft. What do you do?

1. IntegerProgramming Problem
Consider the following integerlinearprogramming problem
Max Z=3x1+2x2
Subject to:
3x1+5x2<=30
5X1+2x2<=28
x1<=8
x1,x2>=0 and integer
The solution to the Linearprogramming relaxation is: x1 = 5.714, x2= 2.571.
What is the Z value for the optimal solution under integer

Assistance with a sample integerlinearprogramming problem.
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 <= 30
4x1 = 2x2 <= 28
x1 <= 8
x1, x2 >= 0 and integer
The solution to the linearprogramming relaxation is x1 = 5.714, x2 = 2.571.
What would be the optimal s

1. Consider the following integerlinearprogramming problem.
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 <= 30
4x1 + 2x2 <= 28
x1 <= 8
x1, x2 >= 0 and integer
The solution to the linearprogramming relaxation is: x1 = 5.714, x2= 2.571.
What is the optimal solution to the integerlinearprogramming problem? State the value

Linearprogramming
Items X1 X2
Profit per Item 3 6
Resource constraints Available Usage Left over
1 7 3 40 0 40
Output
X1= 0
X2= 0
Z= 0
Solve the following linearprogramming model by using the computer
Minimi

1) Consider the following all-integerlinear program
Max 5X1 + 8X2
s.t. 6X1 + 5X2 <= 30
9X1 + 4X2 <= 36
1X1 + 2X2 <= 10
a) Find the optimal solution to the Relaxation LP.
b) Find the optimal solution to the All-inte

Max Z = 5x1 + 6x2
Subject to: 17x1 + 8x2 <= 136
3x1 + 4x2 <= 36
x1, x2 >= 0 and integer
What is the optimal solution? Z = ? Put your answer in the form xx with no additional numbers or symbols.

Explain the characteristics of integerprogramming problems.
Give specific instances in which you would use an integerprogramming model rather than an LP model. Provide real-world examples.
Explain how the applications of Integerprogramming differ from those of linearprogramming.
Why is "rounding-down" an LP solutio