Recall the production model we talked in class Max 10x s.t. 5x = 40 x=0 Suppose
ID: 1248621 • Letter: R
Question
Recall the production model we talked in class Max 10xs.t. 5x = 40 x=0
Suppose the firm considers a second product that has a unit profit of $5 and requires 2 hours of production thime for each unit produced. Use y as the number of units of product 2 produced.
a. Show the mathematical model when both products are considered simultaneously.
b. Identify the controllable and uncontrollable inputs for this model.
c. Draw the flowchart of the input-output process for this model.
d. What are the optimal solution values of x and y?
e. Is the model developed in part a) a deterministic or a stochastic model.
Explanation / Answer
New Model:
Max 10x+5y s.t.
5x+2y<=40
x>=0, y>=0
Profitability from product 1: $10 / 5 hrs
Profitability from product 2: $5 / 2 hrs
Maximum profit will be achieved if all production hours are used to produce product 2.
Optimal solution:
x = 0, y = 20
Objective function = $100
This is a deterministic model. Production hours/ profits per product / total production capacity are known exactly.
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