Compare profit per output barrel

In a petroleum refinery, 2 types of petrol: regular and premium, are obtained by blending naphtha and reformed gasoline in a certain ratio.

The refinery processes 900 barrels of naphtha and 700 barrels of reformed gasoline daily, with no left-over for both naphtha and reformed gasoline. These barrels of oil will either undergo Process 1 to obtain regular petrol or Process 2 to obtain premium petrol.

Process 1: 6 barrels of naphtha and 8 barrels of reformed gasoline are refined to produce 12 barrels of regular petrol.

Process 2: 10 barrels of naphtha and 5 barrels of reformed gasoline are refined to produce 10 barrels of premium petrol.

Using the information above, show that the number of barrels of regular petrol produced daily is 600.

The cost of oil is as follows:

OilNaphthaGasolineRegular PetrolPremium Petrol
Cost / barrel130 dollars100 dollars250 dollars280 dollars

The company’s engineer, Simon, pointed out that the profit earned from sales of premium petrol is lower than that of regular oil. Hence, he suggested that the price of premium petrol should be adjusted to ensure that selling both petrol is equally profitable.

(i) Showing your working clearly, justify that it is more profitable to sell one barrel of regular petrol than selling one barrel of premium petrol. marks

(ii) What should be the new price of the premium petrol to ensure that it is equally profitable to sell it, compared to selling regular petrol? marks

(iii) Explain whether the company will adopt Simon’s suggestion of a price adjustment. marks

[2009/VJC/J1MCT/3]

Total marks: 7

Solution

Q

Linear modelling

A refinery processes 900 barrels of naphtha and 700 barrels of reformed gasoline daily, with none left over. Process 1: 6 barrels of naphtha and 8 of gasoline produce 12 barrels of regular petrol. Process 2: 10 barrels of naphtha and 5 of gasoline produce 10 barrels of premium petrol. Show that the number of barrels of regular petrol produced daily is 600.

Explore this idea

Hint

  1. Let xx and yy be the barrels of regular and premium petrol produced daily.

  2. Naphtha used per barrel of each product: 612\frac{6}{12} and 1010\frac{10}{10}. Gasoline: 812\frac8{12} and 510\frac5{10}.

  3. Total naphtha is 900 and total gasoline 700.

Answer · Q

600 barrels of regular petrol (and 600 premium).

Explore the idea

Two lines, one daily production plan

Each line uses up all of one input. They cross at the production that uses everything.

Switch on a feature to add it to the sketch and see how it is found. A full-mark sketch shows all of them.

  • All production plans that use exactly 900 barrels of naphtha
  • Plans that use exactly 700 barrels of gasoline
  • Unique plan that uses both fully
Ideas to try
Which line is steeper? Why does the gasoline line fall more quickly in regular petrol?
(i)

Profit per unit

The cost of oil is: naphtha 130 dollars/barrel, gasoline 100 dollars/barrel. Regular petrol sells at 250 dollars/barrel and premium at 280 dollars/barrel. Show, with working, that it is more profitable to sell one barrel of regular petrol than one barrel of premium petrol.

Hint

  1. Cost per barrel of product = (input costs of the process) ÷ (barrels produced).

  2. Profit = selling price − cost.

Answer · (i)

Regular profit 11813118\frac13 dollars/barrel; premium 100 dollars/barrel.

(ii)

Pricing

What should be the new price of premium petrol to ensure that selling it is equally profitable compared to selling regular petrol?

Hint

  1. Set the new profit on premium equal to 11813118\frac13 and solve for the price.

Answer · (ii)

29813298\frac13 dollars/barrel.

(iii)

Interpreting a model

Explain whether the company will adopt Simon's suggestion of a price adjustment.

Hint

  1. What could happen to customers if premium petrol costs about 6.5% more?

  2. A model gives equal profit per barrel, but it does not model demand.

Answer · (iii)

No: the higher price may drive customers to other brands and reduce revenue.