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.
A company has determined the demand and supply functions for a product are given by p = D( x) = 14 - x 2 (Demand Function) p = S( x) = 4 x + 2 (Supply Function) where x is the daily quantity and p is in dollars per unit. Find the consumer surplus at the equilibrium point.
Consider the marginal cost function
C′(x)=400+8x−0.01x^2.
a. Find the additional cost incurred in dollars when production is increased from 150 units to 200 units.
b. Find the additional cost incurred in dollars when production is increased from 500 units to 550 units.
The rate at which a solid substance dissolves [dQ/dt] varies directly as the product of undissolved solid present (in the solvent) [A - Q] and as the difference between the saturation concentration [Cs] and the instantaneous concentration [Ci] of the substance.
Let Q - the amount of the substance dissolved at any time t,Let A - the total amount of the substance, then
dQ/dt = (A - Q)(Cs - Ci)
Twenty pounds of salt is dumped into the tank containing 120 lb of solvent, and at the end of 22 minutes, the concentration is observed to be 1 part solute to 30 parts of solvent. Find the amount of solute that is in the solution at any time t, assuming that the saturation concentration is 1 part solute to 3 parts solvent. Answer is shown below.
Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Mathematics for the Trades: A Guided Approach (10th Edition) - Standalone book
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