IM CONFUSED PLEASE HELP! THANK YOU!
2 answers:
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Answer: See linked picture.
Answer:
0.35 cents
Step-by-step explanation:
Let <em>n be the numbers of times the vending company increases in 0.50 dollars the price of its hot dogs</em>, then the income function per game would be
I(n) = (32,000 - 5,000n)(2.50 + 0.50n)
and we have to find the value of n that maximizes the income.
We can write I(n) as a polynomial
Taking the <em>derivative </em>
I'(n) = -5,000n+3,500
I'(n) = 0 when 5,000n=3,500
So n=3,500/5,000 = 0.7
and n=0.7 is a critical point of I
Taking the <em>second derivative</em>
I''(n) = -5,000
Since I''(0.7) = -5,000 < 0 we see n=0.7 is a maximum of I(n)
Hence, the vending company must increase the price 0.7 times 0.5 dollars, that is to say, 0.35 cents.