Compare profit per output barrel · source reference

Printed question

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:

Oil	Naphtha	Gasoline	Regular Petrol	Premium Petrol
Cost / barrel	130 dollars	100 dollars	250 dollars	280 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. [3]

(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? [2]

(iii) Explain whether the company will adopt Simon’s suggestion of a price adjustment. [2]

[2009/VJC/J1MCT/3]

Printed working

Let $x,y$ be the number of barrels of regular and premium petrol respectively.

$\frac6{12}x+\frac{10}{10}y=900$.

$\frac8{12}x+\frac5{10}y=700$.

By GC: $x=600,y=600$.

Thus, number of barrels of regular petrol produced daily is 600. (Shown)

(i) Profit for selling 1 barrel of regular petrol

$=250-\frac{6\times130+8\times100}{12}=118\frac13$ dollars.

Profit for selling 1 barrel of premium petrol

$=280-\frac{10\times130+5\times100}{10}=100$ dollars.

$\therefore$ it is more profitable to sell 1 barrel of regular petrol.

(ii) Let $k$ dollars be the new price of 1 barrel of premium petrol.

$k-\frac{10\times130+5\times100}{10}=118\frac13$.

$\Rightarrow k=298\frac13$.

(iii) The company will not adopt as an increase in the price of premium petrol may lead to customers switching to other brands and hence a decrease in revenue.

Printed answer key

(ii) $298\frac13$ dollars.

(iii) The company will not adopt as an increase in the price of premium petrol may lead to customers switching to other brands and hence a decrease in revenue.

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.