Exam 4: Linear Programming Applications in Marketing, finance, and OM

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Target Shirt Company makes three varieties of shirts: Collegiate,Traditional,and European.These shirts are made from different combinations of cotton and polyester.​ The cost per yard of unblended cotton is $5 and for unblended polyester is $4.Target can receive up to 4000 yards of raw cotton and 3000 yards of raw polyester fabric weekly.The table below gives pertinent data concerning the manufacture of the shirts.​ Target Shirt Company makes three varieties of shirts: Collegiate,Traditional,and European.These shirts are made from different combinations of cotton and polyester.​ The cost per yard of unblended cotton is $5 and for unblended polyester is $4.Target can receive up to 4000 yards of raw cotton and 3000 yards of raw polyester fabric weekly.The table below gives pertinent data concerning the manufacture of the shirts.​   ​ Formulate and solve this blending problem as a linear program.​ ​ Formulate and solve this blending problem as a linear program.​

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A company makes two products,A and B.A sells for $100 and B sells for $90.The variable production costs are $30 per unit for A and $25 for B.The company's objective could be written as: Max 190x1 − 55x2.

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Blending problems occur frequently in which of the following industries?

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Compared to the problems in the textbook,real-world problems generally require more variables and constraints.

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Media selection problems can maximize exposure quality and use number of customers reached as a constraint,or maximize the number of customers reached and use exposure quality as a constraint.

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Linear programming is appropriate for financial problem situations involving capital budgeting,asset allocation,financial planning,and portfolio selection.

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The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative.

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Tots Toys Company is trying to schedule production of two very popular toys for the next three months: a rocking horse and a scooter.Information about both toys is given below. Tots Toys Company is trying to schedule production of two very popular toys for the next three months: a rocking horse and a scooter.Information about both toys is given below.   ​   ​ Develop a model that would tell the company how many of each toy to produce during each month.You are to minimize total cost.Inventory cost will be levied on any items in inventory on June 30,July 31,or August 31 after demand for the month has been satisfied.Your model should make use of the relationship: Beginning inventory + Production − Demand = Ending inventory for each month.The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for September 1.Don't forget to define your decision variables.Tots Toys Company is trying to schedule production of two very popular toys for the next three months: a rocking horse and a scooter.Information about both toys is given below.   ​   ​ Develop a model that would tell the company how many of each toy to produce during each month.You are to minimize total cost.Inventory cost will be levied on any items in inventory on June 30,July 31,or August 31 after demand for the month has been satisfied.Your model should make use of the relationship: Beginning inventory + Production − Demand = Ending inventory for each month.The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for September 1.Don't forget to define your decision variables. ​ Develop a model that would tell the company how many of each toy to produce during each month.You are to minimize total cost.Inventory cost will be levied on any items in inventory on June 30,July 31,or August 31 after demand for the month has been satisfied.Your model should make use of the relationship: Beginning inventory + Production − Demand = Ending inventory for each month.The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for September 1.Don't forget to define your decision variables.

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Meredith Ribbon Company produces paper and fabric decorative ribbon that it sells to paper products companies and craft stores.The demand for ribbon is seasonal.Information about projected demand and production for a particular type of ribbon is given. Meredith Ribbon Company produces paper and fabric decorative ribbon that it sells to paper products companies and craft stores.The demand for ribbon is seasonal.Information about projected demand and production for a particular type of ribbon is given.   ​ An inventory holding cost of $0.005 is levied on every yard of ribbon carried over from one quarter to the next.  a.Define the decision variables needed to model this problem. b.The objective is to minimize total cost,the sum of production and inventory holding cost.Give the objective function. c.Write the production capacity constraints. d.Write the constraints that balance inventory,production,and demand for each quarter.Assume there is no beginning inventory in quarter 1. e.To attempt to balance the production and avoid large changes in the workforce,production in period 1 must be within 5000 yards of production in period 2.Write this constraint. ​ ​ An inventory holding cost of $0.005 is levied on every yard of ribbon carried over from one quarter to the next. a.Define the decision variables needed to model this problem. b.The objective is to minimize total cost,the sum of production and inventory holding cost.Give the objective function. c.Write the production capacity constraints. d.Write the constraints that balance inventory,production,and demand for each quarter.Assume there is no beginning inventory in quarter 1. e.To attempt to balance the production and avoid large changes in the workforce,production in period 1 must be within 5000 yards of production in period 2.Write this constraint. ​

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Portfolio selection problems should acknowledge both risk and return.

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The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources EXCEPT

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Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.

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