Question

It is known that pancake sales at an athletics meeting between a number of schools follow the following pattern: when the price is R3,00 per pancake, 3 000 pancakes are sold during the day and when the price is R2,50 each, 5 000 are sold. Find the demand function with quantity, Q, as a function of price, P. [1] Q = −4P + 15 [2] Q = −4 000P + 15 000 [3] Q = −1 000P + 6 000 [4] Q = 4 000P − 9 000 

Answer 1

Demand function:

$Q=a-bP$

We have:

For Q=3000, P=3.00:

$3000=a-3b$

For Q=5000, P=2.50:

$5000=a-2.5b$

Then:

$2000=0.5b$

$b=4000$

$a=3000+3\cdot4000=15000$

Answer: [2] Q = −4 000P + 15 000