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Also, we must have *0. yz0. Therefore, the above problem can be formulated as follows: find x and y that maximize - 2x + 1.25y subject to the constraints: s 130 3 2 y s 170 y 2 0 Use the technique of linear programming and find feasible region of the problem and locate our extreme points.

Also, we must have *0. yz0. Therefore, the above problem can be formulated as follows: find x and y that maximize - 2x + 1.25y subject to the constraints: s 130 3 2 y s 170 y 2 0 Use the technique of linear programming and find feasible region of the problem and locate our extreme points.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CM: Cumulative Review Problem Set
Problem 115CM
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Q2. (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 - 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: 1 s 130 3 1 s 170 2 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: 1 s 130 3. 2. y 1 s 170 2 y Use the technique of linear programming and find feasible region of the problem and locate our extreme points.
Transcribed Image Text:Q2. (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 - 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: 1 s 130 3 1 s 170 2 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: 1 s 130 3. 2. y 1 s 170 2 y Use the technique of linear programming and find feasible region of the problem and locate our extreme points.
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