$2 There are $288 available to fence in a rectangular garden. The fencing for the side of the garden facing the road costs $6 per foot, and the fencing for the other three sides costs $2 per foot. The picture on the right depicts this situation. Consider the problem of finding the dimensions of the largest possible garden. $2 у $2 (a) Determine the objective and constraint equations. (b) Express the quantity to be maximized as a function of x. (c) Find the optimal values of x and y. $6 Road

$2 There are $288 available to fence in a rectangular garden. The fencing for the side of the garden facing the road costs $6 per foot, and the fencing for the other three sides costs $2 per foot. The picture on the right depicts this situation. Consider the problem of finding the dimensions of the largest possible garden. $2 у $2 (a) Determine the objective and constraint equations. (b) Express the quantity to be maximized as a function of x. (c) Find the optimal values of x and y. $6 Road

Name: There are $288 available to fence in a rectangular garden. The fencin
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: There are $288 available to fence in a rectangular garden. The fencing for the side of the garden facing the road costs $6 per foot, and thefencing for the other three sides costs $2 per foot. The picture on the right depicts this situation. Conside

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...

See similar textbooks

Similar questions

In Example 5, the candy manufacturer improves the production of chocolate-covered creams so that the profit is $2.50 per box. The constraints do not change. What is the maximum monthly profit? How many boxes of each type are produced per month to yield the maximum profit?
A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000
Making furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80
Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.
In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?