   Chapter 7.5, Problem 51E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Biology A lake is to be stocked with smallmouth and largemouth bass. Let x represent the number of smallmouth bass and let y represent the number of largemouth bass. The weight of each fish is dependent on the population densities. After a six-month period, the weight of a single smallmouth bass is given by W 1 =   3   −   0.002 x   −   0.001 y and the weight of a single largemouth bass is given by W 2 =   4.5   −   0.004 x   −   0.005 y . Assuming that no fish die during the six-month period, how many smallmouth and largemouth bass should be stocked in the lake so that the total weight T of bass in the lake is a maximum?

To determine

To Calculate: The number of smallmouth and largemouth bass stocked in the lake to maximize the total weight of bass in the lake.

Explanation

Given Information:

The weight of a single smallmouth bass is,

W1=30.002x0.001y

And the weight of a single largemouth bass is,

W2=4.50.004x0.005y

Where, x represents the number of smallmouth base and y represents the number of largemouth

base.

Formula used:

Total weight written as,

T=xW1+yW2

Calculation:

Consider the information provided as,

The weight of a single smallmouth bass is,

W1=30.002x0.001y

And the weight of a single largemouth bass is,

W2=4.50.004x0.005y

Where, x represents the number of smallmouth base and y represents the number of largemouth

base.

Now the primary equations are,

T(x,y)=x[30.002x0.001y]+y[4.50.004x0.005y]T(x,y)=3x0.002x20.001xy+4.5y0.004xy0.005y2

Further simplifying,

T(x,y)=3x+4.5y0.002x20.005y20.005xy

Differentiating primary equation with respect to x keeping y as constant.

Tx(x,y)=ddy[3x+4.5y0.002x20.005y20.005xy]Tx(x,y)=30.004x0.005y

Differentiating primary equation with respect to y keeping x as constant.

Ty(x,y)=ddy[3x+4.5y0.002x20.005y20.005xy]Ty(x,y)=4

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### limx37x+65x12 = ______. a) 12 b) 75 c) 9 d) 4

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

#### Multiply 56423 .

Mathematics For Machine Technology

#### Identify and describe the steps of the scientific method.

Research Methods for the Behavioral Sciences (MindTap Course List) 