Topic: Linear Programming

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  • 15 Marks

PM – May 2018 – L2 – Q5 – Strategic Management Accounting

Determine the optimal production plan for Classic Wears Plc. and calculate the total profit.

Classic Wears Plc. manufactures three unique jeans wears for which the maximum
revenue for the coming year is estimated as follows:

 

summarised unit cost data are as follows:

 

 

The products are processed on sewing machines housed in a building of three blocks.
Block A contains type I machine which has an estimated maximum of 19,600 machine
hours available in the forthcoming year with fixed overhead cost of N980,000 per
annum.
Block B contains type II machine of which 10,000 machine hours are estimated in the
forthcoming year with a fixed overhead cost of N750,000 per annum.
Block C also contains type II machine which also has an estimate of 8,000 machine
hours available in the forthcoming year. The fixed overhead cost of N370,000 is
estimated per annum for Block C.
The required machine hours for one unit of output for each Jeans on each type of
machine are as follows:

 

 

You are required to:
a. Determine the optimal production plan which Classic Wears Limited should
adopt. (12 Marks)
b. Calculate the total profit that would be made, if the production plan in (a)
above is adopted. (3 Marks)

 

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  • 20 Marks

QT – Nov 2017 – L1 – Q2 – Linear Programming

Formulate and solve a linear programming problem for media advertising to maximize customer reach.

An advertising agency wishes to reach two types of audiences:
Customers with annual income greater than GH¢15,000 (target audience A) and customers with annual income less than GH¢15,000 (target audience B). The total advertising budget is GH¢200,000. One programme on TV advertising costs GH¢50,000; one programme on radio advertising costs GH¢20,000. For contract reasons, at least three programmes ought to be on TV, and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 450,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B.

Required:
i) Formulate the linear programming problem. (4 marks)
ii) Construct the initial simplex tableau. (4 marks)
iii) Perform the first iteration. (4 marks)
iv) Determine the media mix to maximize the total reach. (4 marks)
v) Determine the shadow prices of the binding constraint. (4 marks)

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  • 13 Marks

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

Joycarpap Ltd manufactures and sells three models of affordable toys: Car, Joy, and Pap. Each model requires a specific amount of fabrication hours, material worth, and assembly hours as shown in the table below:

There are 210 fabrication hours available, 170 hours of assembly available, and materials worth GH¢200 in stock. Market research conducted by the company revealed that demand for the toys is such that, in whatever combination of the three models produced, all of the output can be sold within a week.

Each Car contributes GH¢15 to profit, each Joy contributes GH¢20 to profit, and each Pap contributes GH¢14 to profit. Using , ,  as decision variables, and , ,  as slack variables, and  as total profit:

Required:
i) Formulate a linear programming problem. (4 marks)

ii) Set up the initial Simplex Tableau. (4 marks)

iii) Determine the total profit in the first iteration. (5 marks)

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  • 8 Marks

QT – May 2017 – L1 – Q4b – Linear Programming

Formulate a linear programming model for maximizing profit.

Managers within a subsidiary company in a conglomerate want to know how to maximize profit from two types of products, X and Y. Each product X requires one hour of labor and six liters of molding material, whereas each product Y requires two hours of labor and five liters of molding material. The total labor hours available for each week is 40, and the total amount of molding material each week is 150 liters. The profit contribution from product X is GH¢20 and from product Y is GH¢30.

Required:

Formulate the linear programming model for the problem.

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  • 12 Marks

QT – May 2017 – L1 – Q4a – Linear Programming

Graphically represent constraints and determine the optimum solution.

A particular linear programming problem is formulated as follows:

Subject to the constraints:

Required:

i) Draw these constraints on the same graph paper.

ii) Determine the optimum solution.

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  • 20 Marks

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

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  • 15 Marks

PM – May 2018 – L2 – Q5 – Strategic Management Accounting

Determine the optimal production plan for Classic Wears Plc. and calculate the total profit.

Classic Wears Plc. manufactures three unique jeans wears for which the maximum
revenue for the coming year is estimated as follows:

 

summarised unit cost data are as follows:

 

 

The products are processed on sewing machines housed in a building of three blocks.
Block A contains type I machine which has an estimated maximum of 19,600 machine
hours available in the forthcoming year with fixed overhead cost of N980,000 per
annum.
Block B contains type II machine of which 10,000 machine hours are estimated in the
forthcoming year with a fixed overhead cost of N750,000 per annum.
Block C also contains type II machine which also has an estimate of 8,000 machine
hours available in the forthcoming year. The fixed overhead cost of N370,000 is
estimated per annum for Block C.
The required machine hours for one unit of output for each Jeans on each type of
machine are as follows:

 

 

You are required to:
a. Determine the optimal production plan which Classic Wears Limited should
adopt. (12 Marks)
b. Calculate the total profit that would be made, if the production plan in (a)
above is adopted. (3 Marks)

 

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  • 20 Marks

QT – Nov 2017 – L1 – Q2 – Linear Programming

Formulate and solve a linear programming problem for media advertising to maximize customer reach.

An advertising agency wishes to reach two types of audiences:
Customers with annual income greater than GH¢15,000 (target audience A) and customers with annual income less than GH¢15,000 (target audience B). The total advertising budget is GH¢200,000. One programme on TV advertising costs GH¢50,000; one programme on radio advertising costs GH¢20,000. For contract reasons, at least three programmes ought to be on TV, and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 450,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B.

Required:
i) Formulate the linear programming problem. (4 marks)
ii) Construct the initial simplex tableau. (4 marks)
iii) Perform the first iteration. (4 marks)
iv) Determine the media mix to maximize the total reach. (4 marks)
v) Determine the shadow prices of the binding constraint. (4 marks)

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  • 13 Marks

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

Joycarpap Ltd manufactures and sells three models of affordable toys: Car, Joy, and Pap. Each model requires a specific amount of fabrication hours, material worth, and assembly hours as shown in the table below:

There are 210 fabrication hours available, 170 hours of assembly available, and materials worth GH¢200 in stock. Market research conducted by the company revealed that demand for the toys is such that, in whatever combination of the three models produced, all of the output can be sold within a week.

Each Car contributes GH¢15 to profit, each Joy contributes GH¢20 to profit, and each Pap contributes GH¢14 to profit. Using , ,  as decision variables, and , ,  as slack variables, and  as total profit:

Required:
i) Formulate a linear programming problem. (4 marks)

ii) Set up the initial Simplex Tableau. (4 marks)

iii) Determine the total profit in the first iteration. (5 marks)

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  • 8 Marks

QT – May 2017 – L1 – Q4b – Linear Programming

Formulate a linear programming model for maximizing profit.

Managers within a subsidiary company in a conglomerate want to know how to maximize profit from two types of products, X and Y. Each product X requires one hour of labor and six liters of molding material, whereas each product Y requires two hours of labor and five liters of molding material. The total labor hours available for each week is 40, and the total amount of molding material each week is 150 liters. The profit contribution from product X is GH¢20 and from product Y is GH¢30.

Required:

Formulate the linear programming model for the problem.

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  • 12 Marks

QT – May 2017 – L1 – Q4a – Linear Programming

Graphically represent constraints and determine the optimum solution.

A particular linear programming problem is formulated as follows:

Subject to the constraints:

Required:

i) Draw these constraints on the same graph paper.

ii) Determine the optimum solution.

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  • 20 Marks

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

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