A business has found that it can sell 670 items if it sets its price to $66.91. However, if it lowers its price to $43.71, it

Question

A business has found that it can sell 670 items if it sets its price to $66.91. However, if it lowers its price to $43.71, it can sell 950 items.
(a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places)
p(x)=?
It costs the business $11.86 per item to produce and they have $2,150 in overhead each month.
(b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places)
C (x)___x+ _____
R(x)=____x²+ _____x+______
P(x)=____x²+______x+______
(c) Consider the maximum profit the company can make:
To maximize their profit, they should sell _______items at a price of $_______each and they will make $_____ in profit.

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