A company specializing in lubrication products for vintage m

A company specializing in lubrication products for vintage motors produce two blended oils, Smazka and Neftianikov. They make a profit of $5 per litre of Smazka and $4 per litre of Neftianikov. A litre of Smazka requires 0.4 litres of heavy oil and 0.6 litres of light oil. A litre of Neftianikov requires 0.8litres of heavy oil and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of light oil. How many litres of each product should they make to maximize profits? What level of profit will they obtain?

Solution

Let the company produce P liters of Smazka & Q liters of Neft.

So, P liters of Smazka requires 0.4P liters heavy oil & 0.6 liters light oil.

Q liters of Neft requires 0.8Q liters heavy oil & 0.2Q liters light oil.

Total heavy oil required = 0.4P + 0.8Q

Total light oil required = 0.6P + 0.2Q

By question,

0.4P + 0.8Q = 100 ......(1) and

0.6P + 0.2Q = 80 ........(2)

Multiplying (2) by 4, we get

2.4P + 0.8Q = 320 ...... (3)

And

0.4P + 0.8Q = 100 ......(1)

(3) - (1) gives: 2P = 220, or P = 110

Q = [100 - 0.4P] / 0.8 ...... [From (1)]

Q = [100 - 44] / 0.8 = 56 / 0.8 = 70

So, company should make 110 liters of Smazka and 70 liters of Neft.

Total profit = 110 x $5 + 70 x $4 = $550 + $280 = $830