Question

A computer store sells four types of monitors: a 13-inch, a 15-inch, a17-inch and a 19-inch with profit margins of $285, $275, $325 and $250 respectively. As an added feature the store installs on each monitor a privacy filter that narrows the viewing angle so that only the persons sitting directly in front of the monitor can see on-screen data. Each 13-inch monitor requires 20 minutes, each 15-inch monitor requires 25 minutes, each 17-inch monitor requires 30 minutes and 19-inch monitor requires 35 minutes of installation. The store needs to make at least 10 of each model each week. The store has 40 hours of labor time available each week to install privacy screens. The total demand for both monitors is at least 400 monitors per week. The company should make complete units. What is the maximum possible profit for this store selling monitors given these constraints?

$29,175
$30,875
None of the above
$29,000
$27,750
$29,925
$29,875

Answer 1

Decision variables

Let no. of 13 inch monitors produced and sold be x1

Let no. of 15 inch monitors produced and sold be x2

Let no. of 17 inch monitors produced and sold be x3

Let no. of 19 inch monitors produced and sold be x4

Objective

Maximize Z = 285*x1 + 275*x2 + 325*x3 + 250*x4

Constraints

1) 20*x1 + 25*x2 + 30*x3 + 35*x4 <= 2400 {max. labour hours available are 40 hours i.e 2400 minutes}

2) x1 >= 10 {Min. 10 units to be produced each week}

3) x2 >= 10 {Min. 10 units to be produced each week}

4) x3 >= 10 {Min. 10 units to be produced each week}

5) x4 >= 10 {Min. 10 units to be produced each week}

6) x1 + x2 + x3 + x4 <= 400 {demand is 400 per week}

7) x1, x2, x3, x4 >= 0

8) x1, x2, x3, x4 = integers

Even though there is a demand for 400 units each week, the company can only produce a maximum of 105 units because of limited labour hours.

The maximum possible profit is $29,875