Let P(t) denote the profit made by a company when t dollars are invested in advertising. The marginal profit is dP/dt . (a) Explain the meaning of dP dt in practical terms. The expression dP dt is the additional profit expected if 1 more dollar is invested in advertising. The expression dP dt is the total profit expected if t more dollars are invested in advertising. The expression dP dt is the difference between the expected profit and the actual profit. The expression dP dt is the additional profit expected if t more dollars are invested in advertising. The expression dP dt is the total profit expected if 1 more dollar is invested in advertising.
(b) If the marginal profit is positive, should you invest more or less money in advertising

  (a)  (1) The expression dP/dt is the additional profit expected if 1 more dollar is invested in advertising

  (b) you should invest more when dP/dt > 0

Step-by-step explanation:

dP/dt is the rate of change of profit with respect to advertising dollars. That is, it tells the number of dollars the profit will increase if the advertising dollars increase by 1.

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Assuming that the advertising budget is already accounted for in the profit function, it is useful to spend more on advertising if that makes the profit go up. For dP/dt > 0, you should invest more in advertising.

When dP/dt = 0, no more advertising should be purchased. When dP/dt < 0, the advertising budget should be reduced to increase profit.

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