Example: Formulation of Objective and Constraints Giapetto's Woodcarving, Ic., manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier that is manufactured increases Giapetto's variable labor and overhead costs by $14. A train sells for $21 and uses 59 worth of raw materials. Each train built increases Giapetto's variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing and 1 hour of carpentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to formulate an LP to determine the quantity of toys to make each week (x1 and x2, respectively for soldiers and trains) that will maximize his weekly profit. Fill in the following parts accordingly. Remarks: 1. Do not simplify and do not scale any coefficient or function. 2. Each constraint must have a left-hand side (LHS), a right-hand side (RHS) and a relation between LHS and RHS. 3. Relations should be in text format (e.g., >=, =, <=). 4. RHS of each constraint should be a nonnegative numeric value. 5. Do not put any spaces, extra characters or explanations since these may render your answer incorrect. 6. An empty box is considered incorrect and receives zero point. a. Objective and objective function? Objective Objective Function x1 + |x2 b. Constraints? LHS Relation RHS | (Finishing constraint) x1 + x2 x1 + |(Carpentry constraint) x1 + x2 | (Demand constraint) c. Total number of constraints that the LP should have? d. Number of sign/type restrictions?
Example: Formulation of Objective and Constraints Giapetto's Woodcarving, Ic., manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier that is manufactured increases Giapetto's variable labor and overhead costs by $14. A train sells for $21 and uses 59 worth of raw materials. Each train built increases Giapetto's variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing and 1 hour of carpentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to formulate an LP to determine the quantity of toys to make each week (x1 and x2, respectively for soldiers and trains) that will maximize his weekly profit. Fill in the following parts accordingly. Remarks: 1. Do not simplify and do not scale any coefficient or function. 2. Each constraint must have a left-hand side (LHS), a right-hand side (RHS) and a relation between LHS and RHS. 3. Relations should be in text format (e.g., >=, =, <=). 4. RHS of each constraint should be a nonnegative numeric value. 5. Do not put any spaces, extra characters or explanations since these may render your answer incorrect. 6. An empty box is considered incorrect and receives zero point. a. Objective and objective function? Objective Objective Function x1 + |x2 b. Constraints? LHS Relation RHS | (Finishing constraint) x1 + x2 x1 + |(Carpentry constraint) x1 + x2 | (Demand constraint) c. Total number of constraints that the LP should have? d. Number of sign/type restrictions?
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:Example: Formulation of Objective and Constraints
Giapetto's Woodcarving, Inc., manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw
materials. Each soldier that is manufactured increases Giapetto's variable labor and overhead costs by $14. A train sells for S21 and uses $9 worth
of raw materials. Each train built increases Giapetto's variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains
requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires
1 hour of finishing and 1 hour of carpentry labor. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80
carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to formulate an LP to determine the
quantity of toys to make each week (x1 and x2, respectively for soldiers and trains) that will maximize his weekly profit. Fill in the following parts
accordingly.
Remarks:
1. Do not simplify and do not scale any coefficient or function.
2. Each constraint must have a left-hand side (LHS), a right-hand side (RHS) and a relation between LHS and RHS.
3. Relations should be in text format (e.g., >=, =, <=).
4. RHS of each constraint should be a nonnegative numeric value.
5. Do not put any spaces, extra characters or explanations since these may render your answer incorrect.
6. An empty box is considered incorrect and receives zero point.
a. Objective and objective function?
Objective
Objective Function
x1 +
x2
b. Constraints?
LHS
Relation
RHS
x1 +
(Finishing constraint)
х1 +
x2
(Carpentry constraint)
x1 +
x2
(Demand constraint)
c. Total number of constraints that the LP should have?
d. Number of sign/type restrictions?
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