Question

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.

Answer 1

Answer:

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

Answer 2

The correct statement is that to be able to maximize the profits earned, Bata Aerobics Company will have to produce 400 units of luxury steppers and zero units of standard model of steppers.

The calculation of optimum profit earned can be done by putting the given values to the formula for the computation of required quantity to be produced.

Calculation of Profit Maximization

The formula for calculation of profit maximization will be computed as,

$\rm Quantity\ to\ be\ Produced= \dfrac {Total \ Time\ Available}{Time\ per\ unit}$

The contribution per resource will be calculated as, for labor, it will be computed as 4.44 for standard model and 2.5 for luxury model. Whereas, the computation for materials will be 2 and 0.5 for standard and luxury model respectively.

Total available labor minutes are, 3600 and the total time for production of luxury model is 9 minutes per unit.

The total number of units for the production of luxury models will be as below,

$Q(y)= \dfrac {3600}{9}\\\\Q(y)= 400$

The luxury model gives the maximum profit margins so, it will also give the maximum number of profits for the company. So, the standard models are advisable not to be produced.

Hence, the Bata Aerobics Company should produce 400 units of luxury models of steppers and need not produce standard model of steppers to be able to maximize its profits.

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