math
posted by Britney .
The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 digital camera is as follows.
p(x)=0.07x^2+322x96,000
To maximize its profits, how many cameras should Cannon produce each month?
? cameras

dp/dx = .14x = 322
= 0 for max of p
.14x = 322
x = 322/.14 = 2300 
The weekly demand for the Pulsar 25in. color console television is given by the demand equation
p = 0.04 x + 598\ \ \ \ \(0<=x<=12,000\)
where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by
C(x) = 0.000002 x^3  0.01 x^2 + 400x + 80,000
where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest whole number.) 
The weekly demand for the Pulsar 25in. color console television is given by the demand equation
p = 0.04 x + 598\ \ \ \ \(0<=x<=12,000\)
where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by
C(x) = 0.000002 x^3  0.01 x^2 + 400x + 80,000
where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest whole number.)