📚 How to find the maximum using linear programming (Question 4)

Follow us:

Let z=ax+by be an objective function that depends on x and y. Furthermore, z is subject to a number of constraints on x and y. If a maximum or minimum value of z exists, it can be determined as follows:

1. Graph the system of inequalities representing the constraints.
2. Find the value of the objective function at each corner, or vertex, of the graphed region. The maximum and minimum of the objective function occur at one or more of the corner points.

Q. A company manufactures bookshelves and desks for computers. Let x represent the number of bookshelves manufactured daily and y the number of desks manufactured daily. The company’s profits are $25 per bookshelf and $55 per desk. The company should not manufacture more than a total of 80 bookshelves and desks per day. To meet customer demand, the company must manufacture between 30 and 80 bookshelves per day, inclusive. Furthermore, the company must manufacture at least 10 and no more than 30 desks per day. How many bookshelves and how many desks should be manufactured per day to obtain maximum profit? What is the maximum daily profit?