CASE STUDY CHALLENGE

Optimization: Revenue Maximization

A company notes that higher sales of a particular item, which it produced, is achieved by lowering the price charged. As a result, the total revenue from the sales at first rises as the number of units sold increases, reaches the highest point, and then falls off.

The pattern of revenue is described by the relation:

y = 40,00,000 – (x – 2000)2

Where:

  • • y is the total revenue.
  • • x is the number of units sold.

Based on the above information, answer the following questions:

Answer the following:

(a) Find what number of units sold maximizes total revenue. [2]
(b) What is the amount of this maximum revenue? [1]
(c) What would be the total revenue if 2500 units were sold? [1]
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