Question

A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 25 hours of available production time. Work area #2 has 35 hours of available production time. Manufacturing of a door requires 5.3 hours in work area #1 and 3.1 hours in work area #2. Manufacturing of a window requires 4.7 hours in work area #1 and 3.3 hours in work area #2. Profit is $6.50 per door and $3.50 per window.

Show work.

a. Define decision variables that will tell how many units to build (doors and windows).

b. Develop an objective function that will maximize profits.

c. Develop production constrains for work area #1 and #2.

Answer 1

a)

Let X = Number of Doors to be produced
and Y = Number of Windows to be produced
So, X & Y are the decision variables.

b) Let Profit = Z

Objective function is to maximize profit. i.e. Maximize Z.
Z = 6.5 X + 3.5 Y

c)The Constraints are:

5.3 X + 7.1Y <= 25
3.1X + 3.3Y <= 35