SOLUTION: Snookers Lumber can convert logs into either lumber or plywood. In a given day the mill turn out three times as many units of plywood as lumber. It makes a profit of $30 on a unit

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Question 415649: Snookers Lumber can convert logs into either lumber or plywood. In a given day the mill turn out three times as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $50 on a unit of plywood. How many of each unit must be produced or sold to make a profit of 18540
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
L = number of logs
P = number of units of plywood

in a given day, snookers puts out 3 times as many units of plywood as lumber.

you get P = 3*L

profit on lumber = $30 per unit
profit on unit of plywood = $50 per unit.

total profit = 18540

profit equation is:

30*L + 50*P = 18540

you know that P = 3*L

substitute 3*L for P in the profit equation to get:

30*L + 50*3*L = 18540

simplify to get:

30*L + 150*L = 18540

combine like terms to get:

180*L = 18540

divide both sides of equaton by 180 to get:

L = 103

number of logs is equal to 103.

original profit equation is:

30*L + 50*P = 18540

substitute 103 for L to get:

30*103 + 50*P = 18540

simplify to get:

3090 + 50*P = 18540

subtract 3090 from both sides of equation to get:

50*P = 15450

divide both sides of equation by 50 to get:

P = 309

you have:

L = 103
P = 309

original profit equation is:

30*L + 50*P = 18540

substitute for L and P to get:

30*103 + 50*309 = 18540

simplify to get:

3090 + 15450 = 18540

combine like terms to get:

18540 = 18540 which is true confirming the numbers are good.

Snookers Lumber must produce 103 logs and 309 units of plywood to make a profit of 18540


103*30 = 3090
309*50 = 15450
total profit = 18540