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Question

The weekly demand for the Pulsar 25 color LED television is

p=6000.05x(0x12,000)p=600-0.05 x \quad(0 \leq x \leq 12,000)

where pp denotes the wholesale unit price in dollars and xx denotes the quantity demanded. The weekly total cost function associated with manufacturing the Pulsar 25 is given by

C(x)=0.000002x30.03x2+400x+80,000C(x)=0.000002 x^3-0.03 x^2+400 x+80,000

where C(x)C(x) denotes the total cost incurred in producing xx sets.

Compute C(2000),R(2000)C^{\prime}(2000), R^{\prime}(2000), and P(2000)P^{\prime}(2000) and interpret your results.

Solution

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Answered 1 year ago
Answered 1 year ago
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Let's solve given problem.

p=6000.05x(0x12,000)C(x)=0.000002x30.03x2+400x+80,000\begin{aligned} p &= 600 - 0.05x\quad (0\leq x\leq 12,000) \\ C(x) &= 0.000002x^3 - 0.03x^2 + 400x + 80,000 \end{aligned}

In a previous part of this exercise, we derived: C(x)=0.000006x20.06x+400C'(x) = 0.000006x^2 - 0.06x + 400 ; R(x)=6000.1xR'(x) = 600 - 0.1x

C(2000)=0.000006200020.062000+400=304C'(2000)=0.000006\cdot 2000^2-0.06\cdot 2000+400={304}

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