Question

Champion Lumber converts logs into lumber of plywood. In a given week, the total production cannot exceed 800 units. They expect to at least 200 units of lumber and at least 300 units of plywood to their costumers. The profit is $20 on lumber and $30 on plywood. Find the number of units of lumber and plywood that should be produced to maximize profit.

Answer 1

Total Units = TU = L + P <= 800
Lumber Units = L > 200
Plywood Units = P > 300
Profit Lumber = PL = $20/unit
Profit Plywood = PP = $30/unit

First, you know that 500 units are already allocated, so this problem is really just a matter of creating the highest profit from the other 300 units. Since you get higher profit from plywood, and can produce a unit of either plywood or lumber in the same amount of time (assumed), produce all plywood. So the maximum profit would be to create 200 units of lumber and 600 units of plywood.

Total profit = L * PL + P * PP = 200 * 20 + 600 * 30 = 4000 + 18000 = $22000

Answer 2

yessss!! thanks

Answer 3

Anytime.