Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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 10x
s.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.