Question

微积分应用

A retailer notes that for a certain brand of dishwashing liquid, when the price is RM10, the quantity sold per month is 700 and when the price is RM12, the quantity sold per month is 500. If the relationship between price and quantity sold is linear, find the price when the revenue at its maximum.
RM是货币计量单位，同中国的“元”。

Answer 1

记销售量为Q,销售价格为s,由题意，设Q=a*s+b
因为s=10,Q=700; s=12,Q=500
代入解得a=-100,b=1700
即Q=-100*s+1700
revenue=Q*s=(-100*s+1700)*s=-100*(s-8,5)^2+7225
所以当s=RM8,5时，
the revenue reach its maximum 7225