A company produces two products, A and B daily. Each product A and B produced will results RM160 and RM200 in profit, respectively. The production of product A and B is depending on the availability of limited resources. The resource required to produce a unit of product A and B, and the total resources available per day are as follows. a) Resource Requirements Product A Resource Total available per Product B day Labour (hr) Material (kg) Storage (m²) 2 4 40 180 180 2160 240 120 2400 (i) Formulate the linear programming problem. Storage is a non-binding constraint. Solve the linear programming problem simultaneously to obtain the optimal mix and the maximum profit. (ii) (iii) Compute the shadow price of an additional increase in the total labour hours available per day. The overtime payment is RM15 per hour increase in labour hours. Is it worthwhile for the company to increase the total labour hours available per day? Justify your answer.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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b)
Stock Level
200
Time
D
Diagram above shows the stock level of a purchase model for a particular product sold by a
retail store. Given that the quantity ordered results in minimised the total relevant inventory
costs. The stock holding costs are RM18 per year of stock value and the ordering cost is
RM36 on each occasion. Assume that there are 250 working days per year.
(i)
Determine the average stock level of the product.
(ii)
Compute the annual demand of the product.
State two additional assumptions need for above model to determine the total
number of orders per year. Hence find the value of D in the diagram.
(iii)
Transcribed Image Text:b) Stock Level 200 Time D Diagram above shows the stock level of a purchase model for a particular product sold by a retail store. Given that the quantity ordered results in minimised the total relevant inventory costs. The stock holding costs are RM18 per year of stock value and the ordering cost is RM36 on each occasion. Assume that there are 250 working days per year. (i) Determine the average stock level of the product. (ii) Compute the annual demand of the product. State two additional assumptions need for above model to determine the total number of orders per year. Hence find the value of D in the diagram. (iii)
A company produces two products, A and B daily. Each product A and B produced will
results RM160 and RM200 in profit, respectively. The production of product A and B is
depending on the availability of limited resources. The resource required to produce a unit of
product A and B, and the total resources available per day are as follows.
a)
Resource Requirements
Product A
Total available per
day
Resource
Product B
Labour (hr)
Material (kg)
Storage (m²)
2
4
180
240
40
2160
2400
180
120
(i)
Formulate the linear programming problem.
Storage is a non-binding constraint. Solve the linear programming problem
simultaneously to obtain the optimal mix and the maximum profit.
(ii)
Compute the shadow price of an additional increase in the total labour hours
available per day. The overtime payment is RM15 per hour increase in labour hours.
Is it worthwhile for the company to increase the total labour hours available per day?
Justify your answer.
(ii)
Transcribed Image Text:A company produces two products, A and B daily. Each product A and B produced will results RM160 and RM200 in profit, respectively. The production of product A and B is depending on the availability of limited resources. The resource required to produce a unit of product A and B, and the total resources available per day are as follows. a) Resource Requirements Product A Total available per day Resource Product B Labour (hr) Material (kg) Storage (m²) 2 4 180 240 40 2160 2400 180 120 (i) Formulate the linear programming problem. Storage is a non-binding constraint. Solve the linear programming problem simultaneously to obtain the optimal mix and the maximum profit. (ii) Compute the shadow price of an additional increase in the total labour hours available per day. The overtime payment is RM15 per hour increase in labour hours. Is it worthwhile for the company to increase the total labour hours available per day? Justify your answer. (ii)
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