Price–demand. The marginal price dp / dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $1000 per unit [ p (0) = 1000], and there is a weekly demand of 10 units at a price of $367.88 per unit [ p (10) = 367.88]. (A) Find the price–demand equation. (B) At a demand of 20 units per week, what is the price? (C) Graph the price–demand equation for 0 ≤ x ≤ 25.
Price–demand. The marginal price dp / dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $1000 per unit [ p (0) = 1000], and there is a weekly demand of 10 units at a price of $367.88 per unit [ p (10) = 367.88]. (A) Find the price–demand equation. (B) At a demand of 20 units per week, what is the price? (C) Graph the price–demand equation for 0 ≤ x ≤ 25.
Solution Summary: The author calculates that the marginal price is proportional to the price p.
Price–demand. The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $1000 per unit [p(0) = 1000], and there is a weekly demand of 10 units at a price of $367.88 per unit [p(10) = 367.88].
(A) Find the price–demand equation.
(B) At a demand of 20 units per week, what is the price?
(C) Graph the price–demand equation for 0 ≤ x ≤ 25.
The price p (in dollars) and the demand x for a particular clock radio are related by the equation
x=2000−20p.
(A) Express the price p in terms of the demand x, and find the domain of this function.
(B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R?
(C) Find the marginal revenue at a production level of 1200 clock radios.
(D) Interpret R′(1600)=−60.00.
The biological relationship between the growth for the fish population and the size of the fish population is
g = 15S(1-S/5)
where g is the growth of the fish population and S is the size of the population. The size of the harvest is a function of the amount of human effort expended
b = 3ES
where E is the level of effort. Market price of fish per unit is $100 and a constant marginal cost of effort is $50.
The equation representing a sustainable harvest/catch level, b s, in S is b s =
S(1 - S/
).
Mathematics for the Trades: A Guided Approach (10th Edition) - Standalone book
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