College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 6.6, Problem 24E
To determine
To calculate: The maximum and minimum values of the provided objective function
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Management of AG Travel and Tour has identified two groups of individuals that would be interested in the vacation package consisting of room and board and/or entertainment. The maximum amount that group 1 is willing to pay for room and board is GHC 2500 and for entertainment is GHC 500. For group 2, the maximum amount they are willing to pay for room and board is GHC 1800 and for entertainment is GHC 750. Although AG Travel and Tour is not able to identify members of either group, it does know that each group values the components of the package differently. Assuming there are an equal number of members in each group and that the total membership in each group is a single individual. If themarginal cost of providing the service (room and board and/or entertainment) to each group is GHC 1000. i. How much will the hotel charge members of each group for the vacation package if it could identify the members in each group? ii. How much will the profit for AG Travel and Tour be? iii. Since…
The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions.
a.
How much of ingredient 1 will be put into the blend?
b.
How much of ingredient 2 will be put into the blend?
c.
How much of ingredient 3 will be put into the blend?
d.
How much resource A is used?
e.
How much resource B will be left unused?
f.
What will the profit be?
g.
What will happen to the solution if the profit from ingredient 2 drops to 4?
h.
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LINEAR PROGRAMMING…
Read the information below and construct the objective function, and the associated constraint
inequalities. DO NOT SOLVE THE MINIMUM PROBLEM.
The liquid portion of a diet is to provide at least 380 calories, at least 80 units of vitamin A, and
at least 140 units of vitamin C daily. A cup of dietary drink X provides 50 calories, 20 units
of vitamin A, and 30 units of vitamin C. A cup of dietary drink Y provides 40 calories, 30
units of vitamin A, and 90 units of vitamin C. Dietary drink X costs $0.24 per cup and drink
Y costs $0.31 per cup.
Construct the objective function for minimizing the cost, and construct the associated constraint
inequalities to meet the daily dietary requirements by selecting the appropriate symbol or number
from the dropdown list.
Note: The symbol = in
the dropdown list indicates "greater than or equal to".
Cost
=
[Select]
[Select]
20X+ [Select]
[Select]
X+ [Select ]
X + 40Y [Select]
✓Y [Select]
X + 90Y [Select]
✓ Y
✓380
80
140
Chapter 6 Solutions
College Algebra
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Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Graphing an Inequality In Exercises 19-26, use a...Ch. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Writing an Inequality In Exercises 27-30, write an...Ch. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Prob. 55ECh. 6.5 - Writing a System of Inequalities In Exercises...Ch. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Consumer Surplus and Producer Surplus In Exercises...Ch. 6.5 - 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Prob. 45ECh. 6.6 - Prob. 46ECh. 6.6 - Prob. 47ECh. 6.6 - Prob. 48ECh. 6.6 - Prob. 49ECh. 6.6 - Prob. 50ECh. 6.6 - Prob. 51ECh. 6 - Solving a System by Substitution In Exercises...Ch. 6 - Solving a System by Substitution In Exercises...Ch. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Solving a System of Equations Graphically In...Ch. 6 - Solving a System of Equations Graphically In...Ch. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Geometry The perimeter of a rectangle is 68 feet...Ch. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Solving a System by Elimination In Exercises...Ch. 6 - Solving a System by Elimination In Exercises...Ch. 6 - Matching a System with Its Graph In Exercises...Ch. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Matching a System with Its Graph In Exercises...Ch. 6 - 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- Find the maximum value of P=4x+3y subject to the constraints of Example 1. {x+y42x+y6x0y0arrow_forwardA 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 12,000arrow_forwardA) graph the system of inequalities representing the contraints b)find the value of the objetive function at each corner of the graphed region c)use the values in part b to determine the maximum value of the objetive function and the values of x and y at which the maximum occursarrow_forward
- LP Model Formulation Please make sure that your answers in LP Model Formulation are composed of Decision Variables, Objective Function and Constraints. 2. Kraft Company wanted to introduce a new version of Tang. The company will make four types of juice, using lychee, strawberry and mango. There are 200 Kilograms of lychee, 300 Kilograms of strawberry and 400 Kilograms of mango. Kraft wants the ratio of the number of containers of mango juice to the number of containers of lychee juice to be at least 8 to 5. They also wanted strawberry juice to be used for no more than 30 percent of the number of containers produced. Also, they want lychee juice to not exceed one-third of the total product. Formulate an LP model that will determine the number of containers of each product to produce in 1 day to maximize the company's profit. The table below shows the price and the cost per container of juice as well as the kilograms of fruits required to produce one container of juice. Product Mango…arrow_forwardSubject: Math Topic: Linear Programming Instruction: Use a Table for the Data given, Construct the Objective and Constraints Functions, and find the Solution set and Maximize the Sales, and at the end create a graph 1. A Computer Hardware Company produces 2 kinds of CPU Processors : Processor A and Processor B. It takes 2 hours with a cost of P 1500 to manufacture Processor A , while it takes 3 hours with a cost of P 2800 to manufacture Processor B. The Company’s machine can only Operate 345 hours per month and the Company’s Monthly Production Costs Limit is P 300,000 only. Processor A can be sold for P 4500 and Processor B can be sold at P 6500. What is the number of Processor A and Processor B the Company must produce to maximize sales?arrow_forwardFind the minimum and maximum values of the objective function, and the points at which these values occur subject to the given constraints. Objective Function Constraints f(x, y) = 2x + 4y x ≥ 0 y ≥ 0 x + y ≤ 6arrow_forward
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