A shopkeeper has 30 items to sell and want to sell each item at Rs 40 to earn some profit but for every Rs 4 increment in selling price of one item,he left with one unsold item.Find at what selling price, he would be able to maximize his profit? (Some unsold items remain with him).
Answers
Answer:
Selling Price Rs 80
Step-by-step explanation:
A shopkeeper has 30 items to sell and want to sell each item at Rs 40 to earn some profit but for every Rs 4 increment in selling price of one item,he left with one unsold item.Find at what selling price, he would be able to maximize his profit? (Some unsold items remain with him).
30 items to sell
Selling Price = Rs 40 per item
Selling Price = 30 * 40 = 1200
Let say he increase 4n price
then items unsold = 4n/4 = n
Items sold = 30 - n
Price at which items sold = 40 + 4n
Selling Price S = (40 + 4n)(30 - n)
= 4(10 + n)(30 -n)
= 4 ( -n² +20n + 300)
dS/dn = 4 ( -2n + 20)
dS/dn = 0 for maximum value
4 ( -2n + 20) = 0
=> -2n + 20 = 0
=> n = 10
Price increased = 4n = 40
New Selling price = 40 + 40 = Rs 80
Items sold = 30 - 10 = 20
Maximum amount = 80 * 20 = Rs 1600