Snooker's lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12,240?
units of lumber = x
units of ply = 2x
30 x + 45 (2x) = 12240
120 x = 12240
To solve this problem, let's define two variables:
Let's say the number of units of lumber produced is 'L'.
Let's say the number of units of plywood produced is 'P'.
From the given information, we know the following:
1. The mill turns out twice as many units of plywood as lumber:
P = 2L
2. The profit on a unit of lumber is $30 and the profit on a unit of plywood is $45.
Profit from lumber = 30L
Profit from plywood = 45P
3. The total profit is $12,240.
Total profit = 12240
Now we can set up an equation using the information above and solve for L and P.
Profit from lumber + Profit from plywood = Total profit
30L + 45P = 12240
But we also know that P = 2L (from the given information).
30L + 45(2L) = 12240
30L + 90L = 12240
120L = 12240
Dividing both sides of the equation by 120:
L = 12240 / 120
L = 102
Now we can substitute this value back into the equation P = 2L:
P = 2(102)
P = 204
Therefore, in order to make a profit of $12,240, Snooker's lumber mill needs to produce and sell 102 units of lumber (L) and 204 units of plywood (P).