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A company produces two products, A and B. At least 30 units of product [tex]$A$[/tex] and at least 10 units of product [tex]$B$[/tex] must be produced. The maximum number of units that can be produced per day is 80. Product [tex]$A$[/tex] yields a profit of \[tex]$15 and product $[/tex]B[tex]$ yields a profit of \$[/tex]8. Let [tex]$a =$[/tex] the number of units of product [tex]$A$[/tex] and [tex]$b =$[/tex] the number of units of product [tex]$B$[/tex].

What objective function can be used to maximize the profit?

[tex]\[ P = 15a + 8b \][/tex]

(Note: Make sure the function is filled in appropriately based on the given profit values.)



Answer :

GinnyAnswer
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]

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