Question

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.

Answer 1

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

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 for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours  

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative