Expert: Stephen King - 11/22/2004

Question
Your company manufactures two types of laser printers.  The first type, x, takes 55 man-hours to manufacture and earns a profit of $188 for each one sold.  The second type, y, takes 35 man-hours to manufacture and earns a profit of $116 for each one sold.  You only have enough parts to build 100 laser printers of either model this month, and a total of 4200 man-hours to work on them.  Model the objective function and the constraints of this situation.  The graph the feasible region, and find the maximum profit and the number of each type of laser printer that will generate the maximum profit.  (Remember, unfinished printers cannot be sold for a profit.)

Answer
Hello.

I set this up as a system of equations.  Since it doesn't matter which number of unit maximizes the profit, it only matters if the constraints of the number of units and the number of man-hours are met.

x + y = 100
    This is because there is a maximum of 100 printers
55x + 35y = 4200
    This is because the maximum number of man-hours is 4200.

Solve the system of equations:

x = 35
y = 65

If the company builds 35 of type x and 65 of type y, they will maximize their unit building and man-hours.

The now mazimized profit would be:

188 * x = 188 * 35 = 6580
116 * y = 116 * 65 = 7540
6580 + 7540 = 14120

Graphing can be done now that you know the equations.


Steve