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
