Manufacturing Solar Panels Revisited

Problem Definition

Consider the following solution to a daily production mix optimization problem where:

• The decision variables are the number of units to produce of three different types of products

• The objective function coefficients (Objective coefficient in table) are the unitary profits (difference between production costs and sell price per unit) in euros

• The three constraint represent the total availability of three sections in minutes

Decision variables

Decision variable	Solution	Reduced cost	Objective Coefficient	Lower bound	Upper bound
product 1 units	300	0	30	24.44	inf
product 2 units	33.33	0	20	-0	90
product 3 units	0	-8.33	40	-inf	48.33

Constraints

Constraint	Right Hand Side	Shadow Price	Slack	Min RHS	Max RHS
Section 1 availability	400	6.67	0	300	525
Section 2 availability	600	11.67	0	0	800
Section 3 availability	600	0	166.67	433.33	inf

Answer the following questions. Motivate your response based on the provided results:

• Is it profitable to produce units of the three types of products? If any of the products is not profitable, what changes are needed to make it profitable?

• In the actual economic context, the production costs are rising. Discuss how the rise of the production costs can affect your profit and identify the maximum unitary production cost increase that your daily production mix can support without changes in the base solution

• In order to increase your production capacity, you need to evaluate 2 different improvement proposals from an external consultant. The first one considers a 12% increase of the availability of section 1, and the second a 7.5% increase of the availability of section 2. Which one is more profitable for the company?