There has been a lot of soul searching recently at your company, the Beansoul Coal Company (BCC). Some of its better coal mines have been exhausted and it is having more difficulty selling its coal from remaining mines. One of BCC's most important customers is the electrical utility, Power to the People Company (PPC). BCC sells coal from its best mine, the Becky mine, to PPC. The Becky mine is currently running at capacity, selling all its 5000 tons/day of output to PPC. Delivered to PPC, the Becky coal costs BCC $81/ton and PPC pays BCC $86/ton. BCC has four other mines, but you have been unable to get PPC to buy coal from these mines. PPC says that coal from these mines does not satisfy its quality requirements. Upon pressing PPC for details, it has agreed it would consider buying a mix of coal as long as it satisfies the following quality requirements: sulfur < 0.6%; ash < 5.9%; BTU > 13000 per ton; and moisture < 7%. You note your Becky mine satisfies this in that its quality according to the above four measures is: 0.57%, 5.56%, 13,029 BTU, and 6.2%. Your four other mines have the following characteristics:

Mine BTU Per Ton Sulfur% Ash% Mositure% Cost Per Ton

Lex 14201 0.88 6.76 5.1 73

Casper 10630 0.11 4.36 4.6 90

Donora 13200 0.71 6.66 7.6 74

Rocky 11990 0.39 4.41 4.5 89

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)

The following question: 1. At the optimum, What is the actual profit per ton for the coal blend? A.5.82 B. 5.98 C. 7.56 D.6.51 E.6.15

2.Which, if any, of the following mines did not produce coal that was used in the blend? A.Casper B.Donora C. Lex D.Rocky E. All mines was blended.

1. Which of the follwing mines were slack constraints to producing the coal blend? A. Becky B. Casper C. Donora D. Lex E. Rocky

Please show me how to put foluma in Lingo.