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PP-06: Non-linear optimization - Blending models 1. There has been a lot of soul searching recently at your company, the Beansoul Coal Company (BCC)....
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The daily capacities of your Lex, Casper, Donora, and Rocky mines are 4000, 3500, 3000, and 7000 tons respectively. PPC uses an average of about 13,000 tons per day. BCC's director of sales was ecstatic upon hearing of your conversation with PPC. His response was "Great! Now, we will be able sell PPC all of the 13,000 tons per day it needs". Your stock with BCC's newly appointed director of productivity is similarly high. Her reaction to your discussion with PCC was: "Let's see, right now we are making a profit contribution of only $5/ton of coal sold to PPC. I have figured out we can make a profit contribution of $7/ton if we can sell them a mix. Wow! You are an ingenious negotiator!" What do you recommend to BCC? NOTE: The demo version of LINGO is limited to a maximum of 30 non-linear variables (the complete version of this problem has 34). Therefore to accommodate the LINGO demo version limit we will ignore the moisture constraint. This will allow you to develop a non-linear model that can be solved within the non-linear variable limit. (HINT: also, don't forget to include the Becky mine in your solution)
Discussion Questions:
1. What are the decision variables for this problem?
2. There are three possible choices for an objective function:
a. Maximize revenue (which is trivial, since you know the maximum demand and sales price)
b. Minimize cost
c. Maximize profit What would be the difference, if any, between minimizing cost and maximizing profit in this problem?
3. There are also several ways to model the demand constraint: either as a >=, =, or <= . How does the objective function value change among these demand constraints? In other words, is there an advantage to BCC for choosing to satisfy a different demand constraint?
4. You may want to try your hand at developing a linear version of this problem that includes all constraints, and compare it to the non-linear version.
