Ogunquit Craftsmens Guild makes bookcases and desks Each bo

. Ogunquit Craftsmen’s Guild makes bookcases and desks. Each bookcase requires 5 work-hours for assembling and 4 work-hours for finishing. Each desk requires 10 work-hours for assembling and 3 work-hours for finishing. The profit realized per bookcase is $40. The profit realized per desk is $75. The MAXIMUM work-hours available per month for assembling is 600 and for finishing is 240.

How many bookcases and desks should be manufactured each month to make maximum profit? (You may give your answer algebraically or graphically)

What is the associated maximum monthly profit?

Solution

Let no of bookcases = x and no of desks = y

Therefore,

We are to maximise 40x+75y

Such that

5x+10y<=600

4x+3y<=240

x>=0

y>=0

We use the simplex method to solve the problem.

Solving, we get:

x=24, y=48