# 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

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.

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#### 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.