The weekly demand for the Pulsar 40-in. high-definition television is given by t
ID: 3081250 • Letter: T
Question
The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = -0.03 x + 538 (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) = 0.000003 x^3 - 0.03 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.)Explanation / Answer
C(x) = 0.000003 x^3 - 0.03 x^2 + 400x + 80,000
SALES REVENUE = X*P=X[538-0.03X]
GAIN G=X[538-0.03X] - [ 0.000003 x^3 - 0.03 x^2 + 400x + 80,000 ]
DG/DX =538-0.06X-0.000009X^2+0.06X-400 = 0 FOR OPTIMUM
=138-0.000009X^2=0
X=3915.8
X= SAY 3916.....ANSWER
3916 UNITS ARE TO BE PRODUCED
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