How many bookshelves and how many desks should be manufactured per day to obtain a maximum​ profit?

Question

Assume the company makes a profit of​ $15 per bookshelf and​ $40 per desk. They must manufacture between 30 and 70 bookshelves per​ day, inclusive. They must also make between 25 and 65 desks per​ day, inclusive. Let x equal bookshelves and y represent desks. To maintain high​ quality, they should not manufacture more than 90 pieces per day.

The company should manufacture ____ bookshelves and _____desks.

Answer 1

P(B,D) = 15B + 40D

with 30<B<70,

25<D<65,

and B+D < 90

P(30,60) = 15(30) +40(60) = 450+ 2400 = $2,850 profit

P(65,25) = 15(65) + 40(25) = 975 + 1000 = $1,975 profit

P(30,25) =15(30) + 40(25) = 450 + 1000 = $1,450 profit

Maximum profit is with 30 bookshelves and 60 desks $2,850

There is more profit per desk, so maximize the number of desks daily, and minimize the number of bookshelves. 60 is the max for desks as there is a minimum 30 bookshelves. 90-30=60 desks