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Accounting: Objective function and equation

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:

Material P1 P2 P3 Available Quantity
A1 2 1 6 300ea
A2 6 5 1 540ea
A3 4 2 4 320ea

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.