Charles 'n Marge sell custom-build cabinet units for motor homes. The function P(x)=−4.25x2+2300x−8000\displaystyle {P}{\left({x}\right)}=-{4.25}{x}^{{2}}+{2300}{x}-{8000} gives the profit when they build and sell x\displaystyle {x} cabinet units. Find
a) the profit when 75 units are sold
  dollars
b) the average profit per unit as a function of x\displaystyle {x}
  dollars per unit
c) the rate that profit is changing when exactly 75 units are sold
  dollars per unit
d) the number of units that must be sold in order to maximize profit. Round to the nearest whole number if necessary:
units
e) the maximum profit possible (using your whole number answer from part d)
  units

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