Question

Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a certain commodity satisfy the demand equation 6p cubedplusx squaredequals850. Determine the rate at which sales are changing at a time when xequals10​, pequals5​, and the price is falling at the rate of ​$.40 per week.

Answer 1

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Answer:

  increasing 9000 units per week

Step-by-step explanation:

The price and sales relation is given as ...

  6p³ +x² = 850

Differentiating with respect to time gives ...

  18p²·p' +2x·x' = 0

Filling in the given values, we have ...

  18(5)²(-0.40) +2(10)x' = 0

  20x' = 180 . . . . . . add 180

  x' = 9 . . . . . . . . . . divide by 20

Sales are increasing at the rate of 9,000 units per week.