Question

Company A makes 2 models of radios. Model 1 provides a profit of $54 for each unit, while model 2 provides a profit of $72. Two units materials will be required to make one model 1 Radio, while model 2 needs four units. In addition a model 1 takes 4 hours of the time to produce and model 2 takes 5 hours. If 100 units of raw materials and 140 hours of production times are available, how many of each model of Radio will be produced to maximize profit?

Formulate:

a)Objective function

b)Decision variables

c)Constraints

Answer 1

From the given problem:

	Model 1	Model 2	Availability
Raw material	2	4	100
Time in hrs	4	5	140
Profit per radio	$ 54	$ 72

a)

Objective function: since maximize the profit of the company,

Max z = 54 x1 + 72 x2

b) The two decision variables x1 and x2 are defined as below

Let x1 be the number of radios to be manufactured from model-1

Let x2 be the number of radios to be manufactured from model-2

c)

Constrains: 2 x1+ 4 x2 ≤ 100 (constraint on raw material)

                  4 x1+ 5 x2 ≤ 140 (constraint on time to produce a model)

                  x1≥ 0, x2 ≥ 0 . (Non- negativity constraint) Because number radios to be manufactured from two models should be positive in number.