Question

Fairfax Furnaces, Inc. operate a power plant that includes a coal fired boiler to product steam to drive a generator. They are aware that they need to replace the old boiler due to emission issues. The company can purchase four different types of coal from West Virginia and blend them to meet the requirements for burning in the boiler. The following table shows the characteristics of the different types of coal: The required BTU/pound must be at least 11,900. In addition, the ash content can be at most 12.2% and the moisture content can be at most 9.4%. Develop an optimization model to minimize cost which will be in cost per pound. Please do not change the percentage values in the matrix to decimals. The total percentage of the mix, must equal 1. This is a hard problem, please take your time!

Answer 1

Young Energy operates a power plant that includes a coal-fired boiler to produce steam to drive a generator. The company can purchase different types of colas and blend them to meet the requirements for burning in the boiler. The table below shows the characteristics of the different types of coals:

Type of coal	BTU/lb	% Ash	% Moisture	Cost/lb
A	11,500	13%	10%	$2.49
B	11,800	10%	8%	$3.04
C	12,200	12%	8%	$2.99
D	12,100	12%	8%	$2.61

The required BTU/lb must be at least 11,900. In addition, the ash content can be at most 12.2% and the moisture content at most 9.4%.

The company wishes to determine the optimal mix to minimize costs. Thus, we may define:

The objective function is that the company wishes to minimize cost.

From the information provided, maximum BTU/lb must be at least 11,900. The ash content can be at most 12.2% and the moisture content at most 9.4%. Since we want the ratio of A, B, C and D coals in 1 lb of the mixture, their sum must be 1.

In mathematical form, we can write the objective function and constraints as follows:

Subject to the constraints:

The spreadsheet model to solve above problem is shown below.

Now click on DataSolver and fill the dialog box as shown below.

Click on options and fill the dialog box as shown below.

Click on OK and then click on Solve. We get the following result.

From the above result, to minimize the cost, the 1 lb optimal mix should contain only 1 lb of type D coal. The minimum cost of mixture is $2.61/lb.

The sensitivity report is shown below.

The reduced cost tells how much the objective coefficient needs to be reduced in order for a nonnegative variable that is zero in the optimal solution become positive. In the optimal solution, the type A, B and C coals blended in mixture are 0 lb, because it is not economical. If the profit associated with coal A decreased by $2.49, coal B decreased by $3.04, coal C decreased by $2.99, then the optimal solution will change and would include a positive value for the type A, B and C coals.

Please leave a like. Thank you.