What is the fixed cost? fixed cost = dollars What is the maximum profit if each

Question

What is the fixed cost?
fixed cost =  dollars

What is the maximum profit if each item is sold for 6 dollars? (Assume you sell everything you produce.)
maximum profit =  dollars

Suppose we fix production at 34 goods produced, and that they all sell when the price is 6 dollars each. Also suppose that for each 1 dollar increase in price, 1 fewer goods are sold (so if the price is 7 dollars, 33 of the 34 goods being produced are sold.)

To maximize profit in this case, we should   ?    decrease    increase    neither increase nor decrease    the price by  dollars.
(Enter zero if the price should remain at 6 dollars.)

Explanation / Answer

a . the fixed cost is zero , since there is no term independent of q ; b . C ( q ) = 0.01 q^3 - 0.6 q^2 + 14 q ; R ( q ) = 6 q ; Profit = revenue - cost = 6q -( 0.01 q^3 - 0.6 q^2 + 14 q ) = - 0.01 q^3 + 0.6 q^2 - 8 q ; for max profit , P ' ( q ) = 0 ; or -0.01 * 3 q^2 + 0.6 * 2q - 8 = 0 ; or q = 8.4529 , 31.547 ; P '' ( q ) = 6 * ( -0.01 ) q + ( 0.6 * 2 ) = -0.06 q + 1.2 ; P ( 8.4 ) = 0.696 , P ( 31.54 ) = -0.694 ; q = 31.54 is correct for max profit Max profit = - 0.01 * 31.54 ^3 + 0.6 (31.54 ) ^ 2 - 8 ( 31.54 ) = 30.791 ( C ) we sould increase / optimise the price

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