To determine the objective function for maximizing the profit, let's follow these steps:
1. Identify the variables:
- Let [tex]\( a \)[/tex] represent the number of units of product [tex]\( A \)[/tex] produced.
- Let [tex]\( b \)[/tex] represent the number of units of product [tex]\( B \)[/tex] produced.
2. Identify the profit for each product:
- Each unit of product [tex]\( A \)[/tex] yields a profit of [tex]\( \$15 \)[/tex].
- Each unit of product [tex]\( B \)[/tex] yields a profit of [tex]\( \$8 \)[/tex].
3. Formulate the objective function:
- The total profit [tex]\( P \)[/tex] can be expressed as the sum of the profit from product [tex]\( A \)[/tex] and the profit from product [tex]\( B \)[/tex].
Using this information, our objective function [tex]\( P \)[/tex] expressing the total profit from producing [tex]\( a \)[/tex] units of product [tex]\( A \)[/tex] and [tex]\( b \)[/tex] units of product [tex]\( B \)[/tex] is:
[tex]\[ P = 15a + 8b \][/tex]
This is the function you want to use to maximize the profit. Therefore, the complete objective function is:
[tex]\[ P = 15a + 8b \][/tex]
