SOLUTION: John owns a hot dog stand. He has found that his profit is represented by the equation P(x) = [ (-1)x^2 + 62x + 77 ],
with P being profits and x the number of hot dogs sold. How m
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-> SOLUTION: John owns a hot dog stand. He has found that his profit is represented by the equation P(x) = [ (-1)x^2 + 62x + 77 ],
with P being profits and x the number of hot dogs sold. How m
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Question 812303: John owns a hot dog stand. He has found that his profit is represented by the equation P(x) = [ (-1)x^2 + 62x + 77 ],
with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most
profit? Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! y = (-1)x^2 + 62x + 77
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the above quadratic equation is in standard form, with a=-1, b=62, and c=77
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the x coordinate of the max (or min) of the quadratic function is given by: x = -b/2a
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x = -b/2a
x = -62/2(-1)
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x = 31
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the y coordinate of the max (or min) of the quadratic function is found by evaluating the function at the x coordinate of the max (or min)
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y = (-1)x^2 + 62x + 77
y = -(31^2) + 62(31) + 77
y = -(31^2) + 62(31) + 77
y = 1038
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because a < 0 the vertex of the quadratic is a maximum, and (31, 1038) is the maximum.
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Answer:
he must sell 31 to earn the maximum profit of 1038
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