he quantity, q, of a certain bicycle sold by Business Cycle Inc. in a month depends on the
selling price p, in dollars. So q is a function of p. The total revenue, R, is then given by the formula
R = pq.
Suppose that market research at Business Cycle Inc. has determined that a selling price of 250
dollars would yield monthly sales of 6000 bicycles, and that an increase in the selling price by 1
dollar would decrease monthly sales by approximately 20 bikes. This information can be modeled in
mathematical terms as saying that q|p=250 = 6000 and dq
dp |p=250 = −20. Based on this information,
calculate R|p=250 and dR
dp |p=250.
Currently Business Cycle Inc. sells this bike for $250, and the management is discussing whether
it should increase or decrease its price in order to increase revenue. Based on your answers to the
above (that is R|p=250 and dR
dp |p=250), in what direction would you advise the management on this
matter? [Give explanation in support of your answer.]
