6. Write the function that models the situation below: A company produces two types of products: A and B. The profit from producing product A is represented by the function $P_A(x) = 5x$, and the profit from producing product B is represented by the function $P_B(y) = 3y$, where $x$ is the number of product A units produced and $y$ is the number of product B units produced. How much profit does the company make from producing these products?

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6. Write the function that models the situation below: A company produces two types of products: A and B - Leaving Cert Home Economics - Question 6 - 2016

Question 6

6. Write the function that models the situation below: A company produces two types of products: A and B. The profit from producing product A is represented by the ... show full transcript

Worked Solution & Example Answer:6. Write the function that models the situation below: A company produces two types of products: A and B - Leaving Cert Home Economics - Question 6 - 2016

Step 1

Write the profit function for products A and B

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Answer

The total profit function, $P(x, y)$ , for the company can be expressed as the sum of the profits from both products:

$P(x, y) = P_A(x) + P_B(y) = 5x + 3y$

Step 2

Determine specific profit values

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Answer

To find the total profit from producing specific quantities of products A and B, substitute the values of $x$ and $y$ into the profit function. For example, if the company produces 10 units of product A and 15 units of product B:

$P(10, 15) = 5(10) + 3(15) = 50 + 45 = 95$

Thus, the company's profit would be $95.

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