Question

How many units of lumber and plywood must a mill produce to make a $15,080 profit, given a $25 profit per lumber unit, a $40 profit per plywood unit and the mill makes three times as many plywood units as lumber units?

Answer 1

Let \( x \) be the number of lumber units produced. Then, since the mill produces three times as many plywood units, the number of plywood units produced is \( 3x \).

Now, let's calculate the profit from both types of products:

- The profit from lumber units is given by:
\[
\text{Profit from lumber} = 25x
\]

- The profit from plywood units is given by:
\[
\text{Profit from plywood} = 40(3x) = 120x
\]

Now, we can calculate the total profit from both lumber and plywood:
\[
\text{Total profit} = 25x + 120x = 145x
\]

We need this total profit to equal $15,080:
\[
145x = 15,080
\]

To find \( x \), divide both sides by 145:
\[
x = \frac{15,080}{145} = 104
\]

Now, we can calculate the number of plywood units produced:
\[
\text{Plywood units} = 3x = 3(104) = 312
\]

Thus, the mill must produce:
- **Lumber units:** \( 104 \)
- **Plywood units:** \( 312 \)

In summary, the mill must produce 104 units of lumber and 312 units of plywood to make a $15,080 profit.