Question

We have 3,000 Units of product to sell over a five day period. From historical sales data, we have estimated the following demand curves

P=price/unit in $

Q=number of units sold

Day 1: P=10-0.01Q valid for prices between $3and $8.

Day 2: same as Day 1

Day 3: P= 15-0.01Q valid for prices between $6 and $10

Day 4 P=20-0.01Q valid for prices between $6 and $12

Day 5: same as Day 1

1. The revenue maximizing price for day 3 is______ and quantity sold is _______.

2. The revenue maximizing price for day 4 is ______ and quantity sold is _______.

Answer 1

Q. 1). Day 3

P = 15 - 0.01 Q

The revenue maximize when price (P) = $ 6 only.

6 = 15 - 0.01 Q

Q = (15 - 6) / 0.01

Q = 9 / 0.01

Q = 900

Total revenue = P * Q = 6 * 900 = $ 5400.

Accordingly, total revenue is maximum (highest), when price (P) = $ 6 and quantity sold (Q) = 900.

Conclusion :- Price (P) = $ 6 and Quantity sold (Q) = 900.

Q. 2). Day 4

P = 20 - 0.01 Q

The revenue maximize when price (P) = $ 12 only.

12 = 20 - 0.01 Q

Q = (20 - 12) / 0.01

Q = 8 / 0.01

Q = 800

Total revenue = P * Q = 12 * 800 = $ 9600.

Accordingly, total revenue is maximum (highest), when price (P) = $ 12 and quantity sold (Q) = 800.

Conclusion :- Price (P) = $ 12 and Quantity sold (Q) = 800.