A company has the opportunity to produce 3 products (P1; P2; P3) out of 3 Materials (A1; A2; A3). The estimated margin of the products is:
P1= 10$, P2= 6$ and P3= 4$

Please evaluate in which quantity the products have to be produced to show the highest margin possible:

Questions:
A, Establish the objective function and the inequations of this system. Use x1; x2; x3 instead of P1; P2; P3.

B, Create the system of equations and out of it a table for usage of the Simplex Method (just the table no evaluation!)

C, Evaluate the margin by knowing the result will be 65, 30 and 0.

Solution Preview

a) This is a maximization problem.
We are to maximize the total margin M=10x1+6x2+4x3 with constraints
A1: 2x1+x2+6x3<=300
A2: 6x1+5x2+x3<=540
A3: 4x1+2x2+4x3<=320
And ...

Solution Summary

An objective function is analyzed using the Simplex Method. The expert estimates the margin of the product. The opportunity to produce three products are determined.

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

Sketch the region determined by the given constraints. Then find the minimum and maximum values of the objectivefunctionand where they occur, subject to the given constraints. Constraints: y<= -3x+6, y <= -x+3, y>=0, x>=0 and the objectivefunction is z=2x-3y.

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

Consider the following linear programming 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 optimal solution?
c. W

Create your own original Linear Programming problem with a minimum of two variables and two constraints. Your problem should be presented in paragraph form and reflected in a LP equation, showing the objectivefunctionand the constraints.

Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objectivefunction is:
Max 2M + 3B
Min 4000 (M + B)
Max 8000M + 12000B
Min 2M + 3B.

Please see the attached spreadsheet that goes along with the following problem:
One way to solve a linear program is to graph the inequalities to find the feasible region. Next, find the value of the objectivefunction at each of the corner points (i.e., enumerating the corner points).

Consider the following linear programming 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 optimal solution using the graphical solut