Question

Can someone solve this linear programming problem?

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 18 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 $600.00 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?

Answer 1

See below.

Explanation:

Calling

`x_1 =` Num. of bookshelves
`x_2 =` Num. of tables
`c_1 = 20` Cost for each bookshelve
`c_2 = 45` Cost for each table
`p_1 = 60` Profit per bookshelve
`p_2= 100`profit per table

The optimization problem can be stated as

`max p_1x_1+p_2x_2`

subjected to

`x_1 ge 0`
`x_2 ge 0`
`c_1 x_1 + c_2 x_2 le 600`
`x_1 + x_2 le 18`

The resolution is left as an exercise.