Question 1147368
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Revenue R is the product of values of  "q"  and "p"


    R = q*p = q*(128-8q).


In this form, it is a quadratic function of "q", presented as the product of two linear binomials.


The roots of R as the function of "q"  are  q = 0  and  q = {{{128/8}}} = 16.


The maximum value of R as the function of "q"  is exactly half way between the roots.


Thus you found that the maximum of R(q)  is achieved at  q= {{{(0+16)/2}}} = 8.


The value of the maximum is  


    R(8) = 8*(128 - 8*8) = 8*(128-64) = 8*64 = 512.
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