the marginal revenue function for a certain item is given by r'(x)=8x^1/3+3 where x is the number of items. Determine the revenue generated when 27 items are sold if the revenue for 8 items is $50.
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r(x)=integral((8x^(1/3)+3)dx)=(3/4)8x^(4/3)+3x+k, where k is a constant,

When x=8, r(8)=50, so 50=(3/4)8*2^4+24+k; 50=(3/4)8*16+24+k; 96+24+k=50; k=-70.

r(x)=(3/4)8x^(4/3)+3k-70; r(27)=(3/4)8*81+81-70=486+81-70=$497.
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