Question

Car Phones, Inc., sells two models of car telephones: model X and model Y. Records show that 3 hours of sales time are used for each model X telephone that is sold and 5 hours of sales time for each model Y telephone. A total of 600 hours of sales time is available for the next 4 week period. In addition, management planning policies call for minimum sales goals of 25 units for both model X and model Y. The company makes a $40 profit contribution for each model X sold and a $50 profit contribution for each model Y sold.

1. Formulate a mathematical model that can be used to determine the optimal sales goal for the company for the next 4 week period.

2. Develop a spreadsheet formulation and solve.

3. Suppose that management adds the restriction that Car Phones must sell at least as many model Y telephones as model X telephones. What is the new optimal solution?

Answer 1

a.

Let, X = number of units of X model to be sold and Y = number of units of Y model to be sold

objective is to maximize profit Z = Max 40x1+50x2

subject to,

Sales time	3x1	5x2	<=	600
Min sales goal-X	1x1		>=	25
Min sales goal-Y		1x2	>=	25

b.

Solution : X = 158.3333, Y = 25 and maximized profit = 7583.333

Formula used

c.

New restriction would be

Y >= X (Y to be at least equal to X)

So, now the solution becomes X = 75, Y = 75 and Maximized profit = 6750