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A manufacturer produces three models, I, II, and III, of a certain product using raw materials A and B. The following table gives the data for the problem. Requirement per unit Raw material I II III Availability Raw Material A 2 4 7797 Raw Material B 4 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot () to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X = # of unites of model j (j=1,2,3) Objective function: Maximize z = * X,+ X2+ * X3 Subject to: *X1 + 4*X2 + 5*X3 s 4*X1 + *X2 + 8*X3 s Xị + 0.5*X2 + *X3 s 0.25*X1 : 0.5*X2 0.5*X2 *X3 X1 180, X2 X3 250 All variables are non-negative integers.

A manufacturer produces three models, I, II, and III, of a certain product using raw materials A and B. The following table gives the data for the problem. Requirement per unit Raw material I II III Availability Raw Material A 2 4 7797 Raw Material B 4 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot () to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X = # of unites of model j (j=1,2,3) Objective function: Maximize z = * X,+ X2+ * X3 Subject to: *X1 + 4*X2 + 5*X3 s 4*X1 + *X2 + 8*X3 s Xị + 0.5*X2 + *X3 s 0.25*X1 : 0.5*X2 0.5*X2 *X3 X1 180, X2 X3 250 All variables are non-negative integers.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 49P
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Operations research Optimization
Requirement per unit Raw material I II II Availability Raw Material A 4 7797 Raw Material B 4 2 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot (.) to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X; = # of unites of model j (j=1,2,3) Objective function: Maximize z = *X1+ * X2 + * X3 Prev. Next Done II VI
Transcribed Image Text:Requirement per unit Raw material I II II Availability Raw Material A 4 7797 Raw Material B 4 2 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot (.) to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X; = # of unites of model j (j=1,2,3) Objective function: Maximize z = *X1+ * X2 + * X3 Prev. Next Done II VI
A manufacturer produces three models, I, II, and III, of a certain product using raw materials A and B. The following table gives the data for the problem. Requirement per unit Raw material I II III Availability Raw Material A 2 4 5 7797 Raw Material B 4 2 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot (.) to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X; = # of unites of model j (j=1,2,3) Objective function: Maximize z = * X1+ * X2+ * X3 Subject to: *X1 + 4*X2 + 5*X3 s 4*X1 + *X2 + 8*X3 s X1 + 0.5*X2 + *X3 s 0.25*X1 + 0.5*X2 0.5*X2 *X3 X1 + 180, X2 X3 250 All variables are non-negative integers.
Transcribed Image Text:A manufacturer produces three models, I, II, and III, of a certain product using raw materials A and B. The following table gives the data for the problem. Requirement per unit Raw material I II III Availability Raw Material A 2 4 5 7797 Raw Material B 4 2 8 6701 Minimum demand 180 298 250 Price per unit ($) 35 25 55 The labor time per unit of model I is twice that of II and four times that of III. The entire labor force of the factory can produce the equivalent of 1987 units of model I. Market requirements specify the ratios 4:2:5 for the production of three respective models. Complete the LP model of the problem. Note: If any of the answers have decimal points, use a dot (.) to separate them. DON'T use comma or other symbols for the decimals. Decision variables: X; = # of unites of model j (j=1,2,3) Objective function: Maximize z = * X1+ * X2+ * X3 Subject to: *X1 + 4*X2 + 5*X3 s 4*X1 + *X2 + 8*X3 s X1 + 0.5*X2 + *X3 s 0.25*X1 + 0.5*X2 0.5*X2 *X3 X1 + 180, X2 X3 250 All variables are non-negative integers.
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ISBN:
9781337406659
Author:
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