Problema Solution
a recycling company uses scrap cloth and scrap paper to make two different grades of recycled paper. A single batch of grade A recycled paper is made from 25 pounds of scrap cloth and 10 pounds of scrap paper, whereas one batch of grade B recycle paper is made from 10 pounds of scrap cloth and 20 pounds of scrap paper. The company has 100 pounds of scrap cloth and 120 pounds of scrap paper on hand. A batch of grade A paper brings a profit of $500.00 whereas a batch of grade B paper brings a profit of $250.00. What amount of each grade should be made? How, if at all, do the maximum profit and optimal production policy change if the company is required to produce at least one batch of each type
Answer provided by our tutors
Grade A is 2 batch, 2x500=US$1000
Grade B is 5 batch, 5x250=US$1250
The max profite is to produce 2 batch grade A and 5 batch grade B.
Solution: 1 Batch Grade recycled paper = 25p scrap cloth + 10p scrap paper
2 Batch Grade recycled paper = 10p scrap cloth + 20p Scrap paper
The fully use the scrap cloth and Scrap paper, 50p scrap cloth and 20p Scrap paper for 2 batch Grade A, the rest for Grade B.
So the amount of Grade A is 2 batch, 2x500=US$1000
Grade B is 5 batch, 5x250=US$1250