The next three questions are based on the following information. The Low Knock O

Question

The next three questions are based on the following information.

The Low Knock Oil Company produces two grades of cut-rate gasoline for industrial distribution. The grades, regular and economy, are produced by refining a blend of two types of crude oil, type X100 and type X220. Each crude oil differs not only in cost per barrel, but in composition as well. The following table indicates the percentage of crucial ingredients found in each of the crude oils and the cost per barrel for each:

Weekly demand for the regular grade of Low Knock gasoline is at least 25,000 barrels, and demand for the economy is at least 32,000 barrels per week. At least 45% of each barrel of regular must be ingredient A. At most 50% of each barrel of economy should contain ingredient B. While the gasoline yield from one barrel of crude depends on the type of crude and the type of processing used, we will assume for the sake of this example that one barrel of crude oil will yield 0.46 barrel of gasoline.

Hint: You may refer to the Low Knock Oil Company example analyzed on page 326-327 in the textbook (Program 8.9), and simply adjust your constraints for the demands accordingly.

Question 1 of 3

Questiion 2 of 3

Question 3 of 3

CRUDE OIL TYPE INGREDIENT A (%) INGREDIENT B (%) COST/BARREL ($) X100 35 55 30.00 X220 60 25 34.80

Explanation / Answer

The firm lets

X1 = barrels of crude X100 blended to produce the refined regular

X2 = barrels of crude X100 blended to produce the refined economy

X3 = barrels of crude X220 blended to produce the refined regular

X4 = barrels of crude X220 blended to produce the refined economy

nThe objective function is

Minimize cost = $30X1 + $30X2 + $34.80X3 + $34.80X4

At least 45% of each barrel of regular must be ingredient A

(X1 + X3) = total amount of crude blended to produce the refined regular gasoline demand

Thus,

0.45(X1 + X3) = amount of ingredient A required

But

0.35X1 + 0.60X3 = amount of ingredient A in refined regular gas

So

0.35X1 + 0.60X3 0.45X1 + 0.45X3

or

– 0.10X1 + 0.15X3 0 (ingredient A in regular constraint)

Minimize cost = 30X1 + 30X2 + 34.80X3 + 34.80X4

subject to X1 + X3 25,000

X2 + X4 32,000

– 0.10X1 + 0.15X3 0

0.05X2 – 0.25X4 0

              X1, X2, X3, X4 0

At the optimal production, does the company just makeenoughregulargasoline to meet the demand? Does thecompany just make enougheconomygasoline to meet thedemand?

a.Yes, yes

2.Tominimizethe produc±on cost, the op±mal amount ofX100crude oil used inproducingregulargasoline is32609barrels, and the op±mal amount ofX220crude oilused in producingregulargasoline is21739. (Please round to the closestinteger andinclude no units.)

3.Tominimizethe produc±on cost, the op±mal amount ofX100crude oil used inproducingeconomygasoline is57971barrels, and the op±mal amount ofX220crude oil

Low Knock Oil Solution Company X1 X2 X3 X4 RHS DUAL Minimize 30 30 34.8 34.8 Constraint 1 1 0 1 0 >= 25,000 -31.92 Constraint 2 0 1 0 1 >= 32,000 -30.8 Constraint 3 -0.1 0 0.15 0 >= 0 -19.2 Constraint 4 0 0.05 0 -0.25 <= 0 16 SOLUTION> 15,000 26,667.67 10,000 5,333.33 17,83,599.99

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