The Bata Aerobics Company manufactures two models of steppers used for aerobics exercises. To manufacture each luxury model requires 20 lb of plastic and 9 min of labor. To manufacture each standard model requires 30 lb of plastic and 6 min of labor. The profit for each luxury model is $40, and the profit for each standard model is $15. If 12,600 lb of plastic and 60 hr of labor are available for the production of the steppers per day, how many steppers of each model should Bata produce in order to maximize its profits? Let x = number of Luxury Steppers and y = number of Standard Steppers.

to maximize profit it will produce:

400 units of luxury

none of standard.

Explanation:

luxury:

20 lb of pastic and 9 min of labor and 40 dollars profit

standard:

30lb plastic 6 of labor and $15

We calculate the contribution per constrain resourse:

labor hours

40 / 9 = 4.44

15 / 6 = 2.5

materials

40/20 = 2

15 / 30 = 0.5

As luxury provides better contribution in both categories we will maximize his production.

60 hours x 60 min per hours = 3,600 min

3,600 / 9 min = 400 units of luxury steppers

12,600/20 = 630 units of luxury

Once we use the labor hours we cannot keep producing, so we maximize the profit at 400 units of luxury at the given scenario.

As there is no amounft left for standard we don't produce any