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 z = Tx + 1.roy 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 Ir. Also, we must have *2. Y2 Therefore, the above problem can be formulated TX + 1,1o y subiect to the constraints: as follows: find x and y that maximize Use the technique of linear programming and find feasible region of the problem and locate our extreme points. Q6. (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 s 100 hours 3A + 2B s 90 A20, B20
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 z = Tx + 1.roy 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 Ir. Also, we must have *2. Y2 Therefore, the above problem can be formulated TX + 1,1o y subiect to the constraints: as follows: find x and y that maximize Use the technique of linear programming and find feasible region of the problem and locate our extreme points. Q6. (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 s 100 hours 3A + 2B s 90 A20, B20
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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Transcribed Image Text: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
z = Yx + 1.1oy
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:
V < ir.
Also, we must have *2. y2. Therefore, the above problem can be formulated
TX
as follows: find x and y that maximize
+ 1.1oy
subject to the constraints:
S Ir.
y S v.
Use the technique of linear programming and find feasible region of the problem and
locate our extreme points.
Q6.
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 s 100 hours
3A + 2B < 90
A20, B 20
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