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 40 hours of production time are available per week, the following mathematical model defines the total profit earned by selling x units:

Max	10x
s.t.
	5x	≤	40
	x	≥	0

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.

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

   Maximize
   s.t.
   	x ≥ 0, y ≥ 0

2. Identify the controllable and uncontrollable inputs for this model.
   
   Controllable inputs:
   
   Uncontrollable inputs:
3. Fill the flowchart of the input-output process for this model.
   

   Uncontrollable Inputs

   ↓

   →

   Max
   s.t.
   	x ≥ 0
   	y ≥ 0

   →

   Projected Profit and
   check on production
   time constraint

   Controllable
   Inputs

   Mathematical
   Model

   Output

4. What are the optimal solution values of x and y and the corresponding profit? Round the answers for x and y to the nearest whole number. Round the answer for profit to the nearest dollar.
   
   x = fill in the blank 9 units
   
   y = fill in the blank 10 units
   
   Profit = $ fill in the blank 11
5. Is the model developed in part (a) a deterministic or a stochastic model? Explain.

Answer rating: 100% (QA)

a Let y be the number of units of product 2 produced Ob... View the full answer