20.03.2023 - 00:34

Suppose that at the beginning of the year, a Vermont maple syrup distributor found that the demand for maple syrup, sold at $15 a quart, was 500 quarts each month. At that time, the price was going up at a rate of $0.50 a month, but despite this, the dema

Question:

Suppose that at the beginning of the year, a Vermont maple syrup distributor found that the demand for maple syrup, sold at $15 a quart, was 500 quarts each month. At that time, the price was going up at a rate of $0.50 a month, but despite this, the demand was going up at a rate of 30 quarts a month due to increased advertising. How fast was the revenue increasing?

Answers (1)
  • Blanche
    April 8, 2023 в 18:46
    The revenue for the Vermont maple syrup distributor is equal to the price per quart multiplied by the quantity sold. At the beginning of the year, the revenue was $15 * 500 = $7,500 per month. Each month, the price increases by $0.50, so the price per quart at month t is $15 + $0.50t. The demand also increases by 30 quarts a month, so the quantity sold at month t is 500 + 30t. Therefore, the revenue at month t is ($15 + $0.50t) * (500 + 30t). To find how fast the revenue is increasing, we need to find the derivative of the revenue with respect to time t. d(revenue)/dt = $0.50(500 + 30t) + $15(30) = 15t + $7,500 This means that for each month t, the revenue is increasing by $15t + $7,500. For example, at month 1, the revenue is increasing by $7,515, and at month 2, the revenue is increasing by $7,530. Therefore, the revenue is increasing at a rate of $15t + $7,500 per month.
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