Question

In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He figures he has time to make, at most, 25 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $675.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit? A. define variables B. Write the constraint inequalities that represent the situation, and explain what each of the inequalities represents. (You should have four inequalities.) C. What are the vertices of the feasible region?

Answer 1

A. You may set the variables in either order. But for argument sake, let's set as follows:

x = Amount of bookshelves
y = Amount of tables

B. Because of the amount of things you need to make, the following is an inequality using those variables.

x + y > 25

Plus you can determine a second inequality based on the amount of money that you have to spend. 

20x + 45y < 675

Finally you may also add in that each value must be greater than or equal to zero, since they cannot have negative tables. 

C. By solving the system and looking at basic constraints when graphed, you can see the feasible region has 4 vertices. 

(0,0)
(18, 7)
(0, 15)
(33.75, 0) or (33, 0) if you insist on rounding.