SOLUTION: A merchant estimates that he can sell every one of his 60 tomatoes at the current price of 10 cents per tomatoe. For every day that he waits, the price of tomatoes will increase by

Question 321099: A merchant estimates that he can sell every one of his 60 tomatoes at the current price of 10 cents per tomatoe. For every day that he waits, the price of tomatoes will increase by 1 cent each, but the tomatoes will spoil at a rate of 2 per day. If all the tomatoes are sold on the same day, determine how many days he should wait before selling so as to maximize the income from these tomatoes.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A merchant estimates that he can sell every one of his 60 tomatoes at the current price of 10 cents per tomato.
For every day that he waits, the price of tomatoes will increase by 1 cent each,
but the tomatoes will spoil at a rate of 2 per day.
If all the tomatoes are sold on the same day, determine how many days he should
wait before selling so as to maximize the income from these tomatoes.
:
Let x = no. of days and also no. of cents increase
:
Income = no. sold * price
:
I = (60-2x)(10+x)
FOIL
f(x) = 600 + 60x - 20x - 2x^2
A quadratic equation
y = -2x^2 + 40x + 600
Find the axis of symmetry, (x = -b/(2a))
in this equation a=-2, b=40
x =
x =
x = +10
:
He will have max income if you waits until day 10
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