Answer:
Andrew should make 7 tables and 18 bookshelves.
Explanation:
Let the number of tables made = x
Let the number of bookshelves made = y
Therefore:
Andrew has time to make, at most, 25 pieces of furniture by this Saturday.
The materials for each table cost him $45.00.
The materials for each bookshelf cost him $20.00
Total Cost = 45x+20y
Since has $675.00 to spend on materials.
He makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table.
Therefore, the profit function, P(x,y)=100x+60y
Therefore, the required problem is:
<em>Objective Function:</em> Max P(x,y)=100x+60y
Subject to the constraints:
The graph is plotted and the vertices of the feasible region are:
(0,25), (0,0), (7,18) and (15,0).
At (0,25), P(x,y)=100x+60y=100(0)+60(25)=$1500
At (0,0), P(x,y)=100x+60y=100(0)+60(0)=$0
At (7,18), P(x,y)=100x+60y=100(7)+60(18)=$1780
At (15,0), P(x,y)=100x+60y=100(15)+60(0)=$1500
We see that P(x,y) has a maximum at (7,18).
Therefore, to make maximum profit, Andrew should make 7 tables and 18 bookshelves.
