3 math problems

(i need steps.thx)


1.Suppose a product's revenue function is given by R(q)=−8q2+800q , where R(q) is in dollars and q is units sold. Also, it's cost function is given by C(q)=118q+10000 , where C(q) is in dollars and q is units produced. Find a simplified expression for the item's Marginal Profit function (MP(q)) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result).

Answer: MP(q)= _____

2.In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plans of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to:
C(q)=0.02q^2+25.3q+360


where q is the annual quanity of bales (in thousands) produced by the plant. Revenue was estimated at $61 per bale of cotton.

Find the following (but be cautious and play close attention to the units):

A) The Marginal Cost function:
MC(q)=

B) The Marginal Revenue function:
MR(q)=

C) The Marginal Profit function:
MP(q)=

D) The Marginal Profits for q=446 thousand units:
MP(446)= (see Part E for units)

Which of the following represent the proper units for the answer to Part D?
dollars
thousands of dollars per unit
units per dollar
units
dollars per unit
thousands of units per dollar

3.Suppose a revenue function is given by:

R(q)=−q^3+171q

Revenue is maximized for a value of q that takes the form q=sqrt(N), where N is a whole number (no decimals or fractions). Find the value of N.

N=________