(a) Explanation Given Information: The provided revenue function is, R ( t ) = 350 ( 39 t + 68 ) e − 0.3 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: Consider the provided revenue function, R ( t ) = 350 ( 39 t + 68 ) e − 0.3 t Now, differentiate the objective function or the revenue function with respect to t as, R ′ ( t ) = 350 ( 39 ) e − 0.3 t − 0.3 ( 350 ) ( 39 t + 68 ) e − 0.3 t = 350 ( 39 − 11.7 t − 20.4 ) e − 0.3 t = 350 ( 18.6 − 11.7 t ) e − 0.3 t To obtain stationary points, set R ′ ( t ) = 0 as, 350 ( 18.6 − 11.7 t ) e − 0 (b) To determine To calculate: The revenue to the nearest $ 1 million at the time to the nearest when the revenue was projected to peak if the provided revenue function is R ( t ) = 350 ( 39 t + 68 ) e − 0.3 t .

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Question

Chapter 12.2, Problem 53E

(a)

To determine

To calculate: The time to the nearest 0.1 year when the revenue was projected to peak if the provided revenue function is R(t)=350(39t+68)e−0.3t.

(b)

To determine

To calculate: The revenue to the nearest $1 million at the time to the nearest when the revenue was projected to peak if the provided revenue function is R(t)=350(39t+68)e−0.3t.

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Chapter 12.2, Problem 52E

Chapter 12.2, Problem 54E

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The time to the nearest 0.1 year when the revenue was projected to peak if the provided revenue function is R ( t ) = 350 ( 39 t + 68 ) e − 0.3 t .

Solution Summary: The author explains how to solve optimization problems by identifying unknowns, solving the constraint, and finding the absolute maximum or absolute minimum of the objective function.