I have to answer this question for a test, and I always get ZERO because it just confuses me.
"The students of a marketing class determine that they could sell 150 hats at $10 each. Through a survey, they determine that for every $1 increase in price, they will sell 5 fewer hats. Determine the selling price that will maximize revenue."
Help.. Please!
2007-11-03 15:22:17 · 5 answers · asked by Anonymous in Education & Reference ➔ Homework Help
Revenue = price times number sold. Let x = the increase in price. Then 5x = the decrease in sales.
So R = (10+x)(150-5x)
That's 1500 - 50x + 150x - 5x^2
R = 1500 + 100x - 5x^2
This has a maximum at -b over 2a; -100 over 2(-5)
That's -100 over -10 or 10
So increase the price by $10 to $20, selling 50 fewer hats (100)
2007-11-03 15:29:19 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋
At a selling price of 20, they will have $2000 in revenue. Here are the figures from my Excel spreadsheet:
sales price revenue
150 10 1500
145 11 1595
140 12 1680
135 13 1755
130 14 1820
125 15 1875
120 16 1920
115 17 1955
110 18 1980
105 19 1995
100 20 2000
95 21 1995
90 22 1980
85 23 1955
80 24 1920
75 25 1875
70 26 1820
2007-11-03 22:33:27 · answer #2 · answered by hottotrot1_usa 7 · 0⤊ 0⤋
100 hats... 100 x 20 = $2000, the maximum revenue
2007-11-03 22:33:28 · answer #3 · answered by Jim F 2 · 0⤊ 0⤋
sell 100 hats at 20 per
2007-11-03 22:31:27 · answer #4 · answered by Old Goat 3 · 0⤊ 0⤋
125 hats at 15 dollars each.
2007-11-03 22:32:04 · answer #5 · answered by jb 3 · 0⤊ 0⤋