The Charm City Silver Ball Company manufactures three kinds of pinball machines, each requiring a different manufacturing technique. The Super Machine requires 22 hours of labor, 12 hours of testing, and yields a profit of $300. The Silver Ball Special requires 11 hours of labor, 7 hours of testing, and yields a profit of $220. The Bumper King requires 7 hours of labor, 4 hours of testing, and yields a profit of $120. There are 1400 hours of labor and 660 hours of testing available.
The company has made contracts with the retailers to provide at least 22 Super Machines, at least 25 Silver Ball Specials, and at least 30 Bumper Kings.
The manufacturer wants to determine how many of each kind of pinball machines to manufacture. The objective is to maximize the total profit.
Formulate a linear programming model for the above situation by determining
(a) The decision variables (Hint: There are three decision variables for this problem)
(b) The objective function. What does it represent?
(c) All the constraints. What does it represent?