Linear Programming : Objective Function and Optimal Solution

Pet Supplies Company produces 16-ounce cans of dog food by combining meat by-products, which cost $0.60 per pound, and chicken by-products, which cost $0.35 per pound. Meat by-products are 55% protein and 30% fat by weight, while chicken by-products are 40% protein and 10% fat by weight. To meet customer expectations, the final product should contain at least 50% protein and between 15 and 25% fat by weight.

a) Formulate a linear programming solution to be used to determine what the composition of the dog food should be to meet the various requirements at the minimum cost.

b) Using linear programming, find the optimal solution for the objective function and the optimal value of the variables.

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(a) We know, one pound is 16 ounces. Suppose the 16-ounce can of dog food is
combined with x pounds of meat by-products and y pounds of chicken by-products.
Then the objective function is z=0.6x+0.35y, which is the cost of the can.
Now we discuss the restrictions of x and y.
1. The weight of the can is 16 ounces or 1 pound. So ...

Which of the following could be a linearprogrammingobjectivefunction?
Z = 1A + 2B / C + 3D
Z = 1A + 2BC + 3D
Z = 1A + 2B + 3C + 4D
Z = 1A + 2B2 + 3D
all of the above.

Maximize the objectivefunction 2x + 3y subject to the constraints that x + twice y is at most 6; and the sum of 5 times x and 3 times y is at most 15; with both decision variables non-negative.
Find the optimalsolution using linearprogrammingand the graphical solution procedure. What is the value of the objective functio

Consider the following linearprogramming problem:
Max 8X + 7Y
s.t. 15X + 5Y < 75
10X + 6Y < 60
X + Y < 8
X, Y ï?³ 0
a. Set up and solve using Management Scientist, Excel Solver, or an online LP solver.
b. What are the values of X and Y at the optimalsolution?
c. W

1. Consider the following integer linearprogramming 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 optimalsolution to the integer linearprogramming problem? State the value

11. Consider the following linearprogramming problem
Max 8X + 7Y
s.t. 15X + 5Y ï?£ 75
10X + 6Y ï?£ 60
X + Y ï?£ 8
X, Y ï?³ 0
a. Use a graph to show each constraint and the feasible region.
b. Identify the optimalsolution point on your graph. What are the values of X and Y at the optimal s

What is the relationship between decision variables and the objectivefunction?
What is the difference between an objectivefunctionand a constraint?
Does the linearprogramming approach apply the same way in different applications? Explain why or why not using examples.

Consider the following linearprogramming problem:
Min A + 2B
s.t.
A +4B is less than or equal to 21
2A+B is greater than or equal to 7
3A+1.5B is less than or equal to 21
-2A + 6B is greater than or equal to 0
A,B is greater than or equal to 0
1. Find the optimalsolution using the graphical solut

Consider the following linearprogramming problem
Max 8X + 7Y
s.t. 15X + 5Y < 75
10X + 6Y < 60
X + Y < 8
X, Y 0
a. Use a graph to show each constraint and the feasible region.
b. Identify the optimalsolution point on your graph. What are the values of X and Y

In a linearprogramming problem, the binding constraints for the optimalsolution are
5X + 3Y < 30
2X + 5Y < 20.
Fill in the blanks in the following sentence:
As long as the slope of the objectivefunction stays between _______ and _______, the curren