QT – Nov 2016 – L1 – Q6b – Elements of Calculus

Calculate the number of tons of low and high-grade steel to produce to maximize total revenue and determine the maximum total revenue.

Question

Tema Steel Plant is capable of producing tons per day of low-grade steel and tons per day of high-grade steel, where:

If the fixed market price of low-grade steel is GH¢6.90 and the fixed market price of high-grade steel is GH¢13.80:

i) Determine the number of tons of low-grade steel and high-grade steel to be produced to maximize total revenue. (10 marks)

ii) Determine the maximum total revenue. (4 marks)

Answer

i) Total revenue is given by:

$TR (q_{1}, q_{2}) = 6.90 q_{1} + 13.80 q_{2}$

$q_{1} = 14.4721$ and $= 7.236$

ii) The maximum total revenue is:

T Rmax = GH¢199.71

Workings.

i) Total Revenue is given by