King Hussein School of Computing Sciences
Data Science Department
DS14466: Business Intelligence
HW 2
Student Name:
Student ID:
Problem: The profit function for two products is
Profit = −3𝑥12 + 42𝑥1 − 3𝑥22 + 48𝑥2 + 700
where 𝑥1 represents units of production of product 1 and 𝑥2 represents units of production of
product 2. Producing one unit of product 1 requires 4 labor hours and producing one unit of product
2 requires 6 labor hours. Currently, 24 labor hours are available. The cost of labor hours is already
factored into the profit function, but it is possible to schedule overtime at a premium of $5 per
hour. Formulate an optimization problem that can be used to find the optimal production quantity
of products 1 and 2 and the optimal number of overtime hours to schedule. Solve the optimization
model you formulated. How much should be produced and how many overtime hours should be
scheduled?