Question

The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = -0.04x + 561 (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) = 0.000001x^3 - 0.01x^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 40-in. high-definition television is given by the demand equation
p = -0.04x + 561 (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) = 0.000001x^3 - 0.01x^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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The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation
p = -0.04x + 561 (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) = 0.000001x^3 - 0.01x^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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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = -0.04x + 561 (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) = 0.000001x^3 - 0.01x^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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The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = -0.04x + 561 (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) = 0.000001x^3 - 0.01x^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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The weekly demand for the Pulsar 40 -in. high-definition television is given by the demand equation $p=-0.05 x+600 \quad(0 \leq x \leq 12,000)$ 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 $$ \begin{array}{l} \text { If } C(x)=0.000002 x^{3}-0.03 x^{2}+400 x+80,000 \\ \text { ( } x=0,00002 x^{3}-0,00 x+0000=00000000000000000000000000000000000000 \\ \text { (?) } 6,0000 \end{array} $$ 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.

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the-weekly-demand-for-the-pulsar-40-in-high-definition-television-is-given-by-the-demand-equation-p-60362

The weekly demand for the Pulsar 40 -in. high-definition television is given by the demand equation $p=-0.05 x+600 quad(0 leq x leq 12,000)$ 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 $$ C(x)=0.000002 x^{3}-0.03 x^{2}+400 x+80,000 $$ 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.

Madhur L.


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Transcript

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00:01 High in this problem we are given the demand equation p equal to minus 0 .05x plus 586 and where x is between 0 ,000.
00:15 Now further we are given the cost function c of x equal to 0 .00004 x cube minus 0 .04 x squared minus 0 .04 x squared plus 400 x plus 80 ,000 and we are required to find out the level of production that will yield a maximum profit for the manufacturer.
00:45 So first the revenue that is r of x is equal to xpx and further putting all the values and solving this is equal to minus 0 .05 x square plus 586 x x now the marginal revenue is equal to r -dash of x.
01:13 So differentiating r -x, we obtain r -dash -of -x equal to minus 0 .1x plus 586.
01:24 Further, the marginal cost is equal to c -of -x.
01:33 So therefore, differentiating c -x, we obtain c -dash -of -x equal to.
01:38 To 0 .0001 2x square minus 0 .08 x plus 400...
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