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If we let x represent the number of units sold and P the total profit, then, wit

ID: 351561 • Letter: I

Question

If we let x represent the number of units sold and P the total profit, then, with a profit of $10 per unit, assuming that 5 hours are required to produce each unit and only 50 hours of production time are available per week, the following mathematical model defines the total profit earned by selling x units:

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time for each unit produced. Use y as the number of units of product 2 produced.

Show the mathematical model when both products are considered simultaneously. Express your answers in terms of x and y.

Identify the controllable and uncontrollable inputs for this model.

Controllable inputs:

Uncontrollable inputs:

Fill the flowchart of the input-output process for this model.

What are the optimal solution values of x and y? Round the answers for x and y to the nearest whole number. Round the answer for profit to the nearest dollar.

x =  units

y =  units

Profit = $   

Is the model developed in part (a) a deterministic or a stochastic model? Explain.

The model is .

Max   10x s.t. 5x 50 x 0

Explanation / Answer

Hours available per week = 50 hours

Product 1 = 1 unit of product needs 5 hpurs of production time.

Therefore, In a week , 10 units of product 1 will be manufactured. Profit per unit is $10 , thus profit for product 1 is $100.

For product 2, 2 hours are required for manufacturing per unit.

In a week, 25 units will be manufactured. Profit @$5 per unit will be $125 .

The study shows comparitive profitability of rhe two products with available time per week.

Controllable inputs : production of product 1 or product 2, quantity of units produced for two products.

Uncontrollable input : production time constraints.

The model will be a deterministic model.

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