Question

A company produces and sells two types of coolants (C1 and C2) by mixing three grades of solvents (A, B, and C) in different proportions.

Minimum percentages of grade A solvent and maximum percentages of grade C solvent allowed for each type of coolant are specified. The company has to produce at least a specified minimum quantity of each type of coolant. The table below presents these requirements, along with the selling price of each type of coolant.

	Minimum percent of grade A allowed	Maximum percent of grade C allowed	Minimum Quantity Required (gallons)	Selling price per gallon
C1	50%	20%	200,000	$6
C2	30%	50%	200,000	$4

Availability of the three grades of solvents and their costs are as follows:

Grade	A	B	C
Maximum quantity available per day (gallons)	200,000	124,000	156,000
Cost per gallon	$4	$3	$2

The company wants to maximize profits subject to the specified constraints.

Formulate the problem as a linear program, find the optimal solution, and answer the following questions:

1. What is the maximum profit attainable? [3 Points]

The maximum profit attainable is $ ……………….

2. How many gallons of each solvent are used to produce each type of coolant under the optimal solution? [3 points]

Gallons used	grade A	grade B	grade C
In C1
In C2

3. At most how much should the company be willing to pay for one additional gallon of grade A solvent (beyond its current availability of 200,000 gallons)? [6 points]

The refinery should be willing to pay up to $ …………. for an additional gallon of the grade A distillate over 200,000 gallon.

Answer 1

According to the question,

THE SOLVER SETUP SHOWN IN BELOW,

FORMULAS,

SOLVER PARAMETERS,

RESULT,

THE SENSITIVITY ANALYSIS REPORT SHOWN ON BELOW,

A.The maximum profit attainable = $996000

B.The coolant mix is shown below

	A	B	C
C1	140000	84000	56000
C2	60000	40000	100000

C.The solvent A relates to Const 7. This means the shadow price for solvent A is 2. Every 1 unit increase in the constraint’s RHS will result in a positive impact of 2 in the final profit. This means the refinery should be willing to pay at most $2 per gallon for additional solvent A.