The daily cost, in dollars, to produce x Sasquatch Berry Pies is C(x) = 3x + 36, x ≥ 0 and
the price-demand function, in dollars per pie, is p(x) = 12 − 0.5x, 0 ≤ x ≤ 24. Find the price to charge per item in order to maximize profit.
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rafikiedu08 3 weeks ago
Светило науки - 2186 ответа - 0 помощи

The cost per item for maximum profit is \$7.50 .

The maximum and minimum value of a function f(x) is calculated by finding the first and second derivative of f(x).

• If f"(x)<0 then the function f(x) has a maximum value for x at f'(x)=0.
• If f"(x)>0 then the function f(x) has a minimum value for x at f'(x)=0.

The cost to produce x pies is given by the cost function The price demand function for each pie is given by Revenue gained from selling x pies Now profit function is given by Now we have to find the maximum profit. We know that for a function  At P'(x)=0

or,-x+9=0

or, x=9

As P''(x)<0 therefore the profit function P(x) is maximum for x at P'(x)=0.

The profit is maximum at x=9

Price to charge per item=12-0.5x

Substituting the value of x we get: Therefore the cost per item for maximum profit is \$7.50 .

To learn more about maximum and minimum value of a function: