Explanation Given Information: The total value of its collection of 1959 Chevrolets and Fords is given by v = 300 , 000 + 1000 t 2 ( t ≥ 5 ) , Where t is the number of years from now. A continuous inflation rate of 5 % per year is anticipated so that the present value of an item that will be worth $ v in t years’ time is, p = v e − 0.05 t Formula used: Steps to solve optimization problems: Step 1: Identify the unknowns with the aid of diagram. Step 2: Identify the objective function, the quantity to maximize or minimize. Step 3: Identify the constraint, the equations relating variables or inequalities expressing limitations on the value of the variables. Step 4: State the optimization problem Step 5: Eliminate the extra variables, solve the constraint for one unknown and substitute in the objective function. Step 6: Find the absolute maximum or absolute minimum of the objective function. Calculation: As it is provided that the total value of its collection of 1959 Chevrolets and Fords is given by v = 300 , 000 + 1000 t 2 ( t ≥ 5 ) , Where t is the number of years from now. A continuous inflation rate of 5 % per year is anticipated so that the present value of an item that will be worth $ v in t years’ time is, p = v e − 0.05 t Substitute 300 , 000 + 1000 t 2 for v in above function to get, p = ( 300 , 000 + 1000 t 2 ) e − 0.05 t , ( t ≥ 5 ) Now, differentiate the objective function p = ( 300 , 000 + 1000 t 2 ) e − 0.05 t with respect to t as, p ′ = 2000 t e − 0

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 12.2, Problem 57E

To determine

To calculate: The optimal time to advice the dealership to sell the vehicles to maximize their discounted value if the total value of its collection of 1959 Chevrolets and Fords is given by v=300,000+1000t2 (t≥5), a continuous inflation rate of 5% per year is anticipated so that the present value of an item that will be worth $v in t years’ time is p=ve−0.05t

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.2, Problem 56E

Chapter 12.2, Problem 58E

Students have asked these similar questions

2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the mixture is allowed to flow out of the tank at a rate of 3 gal/min. a. Find the amount of salt in the tank at any time prior to the instant when the tank begins to overflow (650 gallons). b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits 400 gallons. D.E. for mixture problems: dv dt=11-12 dA A(t) dt

- Suppose that you have the differential equation: dy = (y - 2) (y+3) dx a. What are the equilibrium solutions for the differential equation? b. Where is the differential equation increasing or decreasing? Show how you know. Showing them on the drawing is not enough. c. Where are the changes in concavity for the differential equation? Show how you know. Showing them on the drawing is not enough. d. Consider the slope field for the differential equation. Draw solution curves given the following initial conditions: i. y(0) = -5 ii. y(0) = -1 iii. y(0) = 2

5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1

Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Solution Summary: The author calculates the optimal time to advise the dealership to sell the vehicles to maximize their discounted value if the total value of its collection of 1959 Chevrolets and Fords is given by v=300,000+1000

Concept explainers

Videos

Want to see the full answer?

Chapter 12 Solutions