# math

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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+322x-96,000

To maximize its profits, how many cameras should Cannon produce each month?

? cameras

• math -

dp/dx = -.14x = 322
= 0 for max of p
.14x = 322
x = 322/.14 = 2300

• math -

The weekly demand for the Pulsar 25-in. 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.)

• math -

The weekly demand for the Pulsar 25-in. 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.)

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