A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for $2.00 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.25 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue? let us call A the mixture of half cherries and half mints, and B the mixture which is one-third cherries and two-thirds mints. Let x be the number of pounds of A to be prepared and y the number of pounds of B to be prepared. The revenue function can then be written as Since each pound of A contains one-half pound of cherries and each pound of B contains one-third pound of cherries, the total number of pounds of cherries used in both mixtures is Similarly, the total number of pounds of mints used in both mixtures is: Now, since the manufacturer can use at most 130 pounds of cherries and 170 pounds of mints, we have the constraints: Also, we must have Therefore, the above problem can be formulated as follows: find x and y that maximize subject to the constraints: Use the technique of linear programming and find feasible region of the problem and locate our extreme points.Q 6. (B)Make a linear programming graph from the following LP model and find out the most profitable solution.Maximize CM = $25A + $40BSubject to: 2A + 4B ≤ 100 hours 3A + 2B ≤ 90 A ≥ 0, B ≥ 0 (b)What is the firm's profit maximizing output level?(c) Is the industry in long-run equilibrium? Justify your answer.О6. (А)A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mintsin stock. He decides to sell them in the form of two differentmixtures. One mixture will contain half cherries and halfmints by weight and will sell for $2.00 per pound. The othermixture will contain one-third cherries and two-thirds mintsby weight and will sell for $1.25 per pound. How manypounds of each mixture should the candy manufacturerprepare in order to maximize his sales revenue?let us call A the mixture of half cherries and half mints, and Bthe mixture which is one-third cherries and two-thirds mints.Let x be the number of pounds of A to be prepared and y thenumber of pounds of B to be prepared. The revenue functioncan then be written as2 - 2x + 1.25ySince each pound of A contains one-half pound of cherriesand each pound of B contains one-third pound of cherries, thetotal number of pounds of cherries used in both mixtures isSimilarly, the total number of pounds of mints used in bothmixtures is:Now, since the manufacturer can use at most 130 pounds ofcherries and 170 pounds of mints, we have the constraints:s 130s 170Also, we must have *20, y20. Therefore, the above problemcan be formulated as follows: find x and y that maximize- - 2x + 1.25y subject to the constraints:y s 130s 170Use the technique of linear programming and find feasibleregion of the problem and locate our extreme points.Q 6.Make a linear programming graph from the following LPmodel and find out the most profitable solution.(В)Maximize CM = $25A+ $40BSubject to: 2A + 4B < 100 hours3A + 2B < 90A2 0, B >0

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Description: A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and w

Q6(A) The linear programming problem is Max Z= 2x + 1.25 ySubject to , x2 + y3≤130 ......(1)…

Q 6. (A) A candy manufacturer has 130 pounds of chocolate- covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for $2.00 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.25 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue? let us call A the mixture of half cherries and half mints, and B the mixture which is one-third cherries and two-thirds mints. Let x be the number of pounds of A to be prepared and y the number of pounds of B to be prepared. The revenue function can then be written as : - 2x + 1.25 y Since each pound of A contains one-half pound of cherries and each pound of B contains one-third pound of cherries, the total number of pounds of cherries used in both mixtures is Similarly, the total number of pounds of mints used in both mixtures is: Now, since the manufacturer can use at most 130 pounds of cherries and 170 pounds of mints, we have the constraints: 1 s 130 s 170 Also, we must have *0. y20. Therefore, the above problem can be formulated as follows: find x and y that maximize : - 2x + 1.25y subject to the constraints: y s 130 3' s 170 Use the technique of linear programming and find feasible region of the problem and locate our extreme points. Q 6. (В) Make a linear programming graph from the following LP model and find out the most profitable solution. Maximize CM= $25A+ $40B Subject to: 2A + 4B< 100 hours 3A+ 2B < 90 A20, B 20

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for $2.00 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.25 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue? let us call A the mixture of half cherries and half mints, and B the mixture which is one-third cherries and two-thirds mints. Let x be the number of pounds of A to be prepared and y the number of pounds of B to be prepared. The revenue function can then be written as Since each pound of A contains one-half pound of cherries and each pound of B contains one-third pound of cherries, the total number of pounds of cherries used in both mixtures is Similarly, the total number of pounds of mints used in both mixtures is: Now, since the manufacturer can use at most 130 pounds of cherries and 170 pounds of mints, we have the constraints: Also, we must have Therefore, the above problem can be formulated as follows: find x and y that maximize subject to the constraints: Use the technique of linear programming and find feasible region of the problem and locate our extreme points. Q 6. (B) Make a linear programming graph from the following LP model and find out the most profitable solution. Maximize CM = $25A + $40B Subject to: 2A + 4B ≤ 100 hours 3A + 2B ≤ 90 A ≥ 0, B ≥ 0

(b)What is the firm's profit maximizing output level?
(c) Is the industry in long-run equilibrium? Justify your answer.
О6. (А)
A candy manufacturer has 130 pounds of chocolate-
covered cherries and 170 pounds of chocolate-covered mints
in stock. He decides to sell them in the form of two different
mixtures. One mixture will contain half cherries and half
mints by weight and will sell for $2.00 per pound. The other
mixture will contain one-third cherries and two-thirds mints
by weight and will sell for $1.25 per pound. How many
pounds of each mixture should the candy manufacturer
prepare in order to maximize his sales revenue?
let us call A the mixture of half cherries and half mints, and B
the mixture which is one-third cherries and two-thirds mints.
Let x be the number of pounds of A to be prepared and y the
number of pounds of B to be prepared. The revenue function
can then be written as
2 - 2x + 1.25y
Since each pound of A contains one-half pound of cherries
and each pound of B contains one-third pound of cherries, the
total number of pounds of cherries used in both mixtures is
Similarly, the total number of pounds of mints used in both
mixtures is:
Now, since the manufacturer can use at most 130 pounds of
cherries and 170 pounds of mints, we have the constraints:
s 130
s 170
Also, we must have *20, y20. Therefore, the above problem
can be formulated as follows: find x and y that maximize
- - 2x + 1.25y subject to the constraints:
y s 130
s 170
Use the technique of linear programming and find feasible
region of the problem and locate our extreme points.
Q 6.
Make a linear programming graph from the following LP
model and find out the most profitable solution.
(В)
Maximize CM = $25A+ $40B
Subject to: 2A + 4B < 100 hours
3A + 2B < 90
A2 0, B >0

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