A candy manufacturer has 130 pounds of chocolate-covered chenies and 170 pounds ofchocolate-covered mints in stock. He decides to sell them in the form of two differentmixtures. One mixture will contain half cheries and half mints by weight and will sell for$2.00 per pound. The other mixture will contain one-third cheries and two-thirds mints byweight and will sell for $1.25 per pound. How many pounds of each mixture should thecandy manufacturer prepare in order to maximize his sales revenue?let us call A the mixture of half cheies and half mints, and B the mixture which is one-third chenries and two-thirds mints. Let x be the number of pounds of A to be prepared and ythe number of pounds of B to be prepared. The revenue function can then be written as: = 2x + 1.25 ySince each pound of A contains one-half pound of chenies and each pound of B containsone-third pound of chenries, the total number of pounds of chenies used in both mixtures is1x +1Similarly, the total number of pounds of mints used in both mixtures is:1Now, since the manufacturer can use at most 130 pounds of chenies and 170 pounds ofmints, we have the constraints:-y< 1301< 170++ Also, we must have *20, y 20. Therefore, the above problem can be formulated as= 2x + 1.25y subject to the constraints:follows: find x and y that maximize1< 130-y3< 1702 0y 2 0Use the technique of linear programming and find feasible region of the problem and locateour extreme points.Q 6.(B)Make a linear programming graph from the following LP model and find out the mostprofitable solution.Maximize CM = $25A + $40BSubject to: 2A + 4B < 100 hours3A + 2B < 90A2 0, B20

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Also, we must have *20. y20. Therefore, the above problem can be fomulated as follows: find x and y that maximize - = 2x + 1.25y subject to the constraints: y < 130 -x 3* 2 y < 170 2 0 y 2 0 +

Also, we must have 20. y20. Therefore, the above problem can be fomulated as follows: find x and y that maximize - = 2x + 1.25y subject to the constraints: y < 130 -x 3 2 y < 170 2 0 y 2 0 +

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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Topic Video

Question

A candy manufacturer has 130 pounds of chocolate-covered chenies 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 cheries and half mints by weight and will sell for
$2.00 per pound. The other mixture will contain one-third cheries 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 cheies and half mints, and B the mixture which is one-
third chenries 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 chenies and each pound of B contains
one-third pound of chenries, the total number of pounds of chenies used in both mixtures is
1
x +
1
Similarly, the total number of pounds of mints used in both mixtures is:
1
Now, since the manufacturer can use at most 130 pounds of chenies and 170 pounds of
mints, we have the constraints:
-y
< 130
1
< 170
+
+

Also, we must have *20, y 20. Therefore, the above problem can be formulated as
= 2x + 1.25y subject to the constraints:
follows: find x and y that maximize
1
< 130
-y
3
< 170
2 0
y 2 0
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
A2 0, B20

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