Snookers Lumber can convert logs into either lumber ofr lywood. In a given day, the mill turns out three times as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $40 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $15600?
x units of lumber.
3x units of plywood.
30x + 40*3x = $15,600,
150x = 15,600,
X = 104 Units of lumber.
3X = 312 Units of plywood.
To solve this problem, we can set up a system of equations. Let's denote the number of units of lumber as L and the number of units of plywood as P.
Given that the mill turns out three times as many units of plywood as lumber, we can write the equation:
P = 3L (Equation 1)
We also know that the profit on a unit of lumber is $30 and on a unit of plywood is $40. Therefore, the total profit can be expressed as:
30L + 40P = 15600 (Equation 2)
To solve this system of equations, we can substitute the value of P from Equation 1 into Equation 2:
30L + 40(3L) = 15600
Simplifying the equation:
30L + 120L = 15600
150L = 15600
L = 104
Now that we have the value of L, we can substitute it back into Equation 1 to find P:
P = 3(104)
P = 312
Therefore, in order to make a profit of $15,600, the mill needs to produce and sell 104 units of lumber and 312 units of plywood.