A small company produces only two sizes of frames for stereo receivers: standard size
and slim-line. The accounting department has provided the following analysis of the
unit profit:
Standard Slim-line
Selling price Sh. 6.00 Sh. 4.25
Raw materials Sh. 0.75 Sh. 0.50
(1.5 units @ Sh.
0.50/unit)
(1 unit @ Sh. 0.50/unit)
Packaging Sh. 0.25 Sh. 0.25
Labour 0.40 hours 0.25 hours
Labour is considered a fixed cost as it is performed by salaried workers at the plant.
There are 350 units of the raw materials and 300 packing boxes available daily. Both
products utilize the same packing boxes. At most 10 workers (at 8 hours/day) will be
assigned to this project. This problem was solved by the management scientists
software with part of the output shown below.
Variable Value Reduced
Cost
Standard 33.333 0.000
Slim-line 266.667 0.000
Constraint Slack/surplus Dual prices
Raw materials 33.333 0.000
Packaging boxes 0.000 1.000
Labour 0.000 10.000
Objective Coefficient ranges
Variable Lower limit Upper limit
Standard (C1) 3.500 5.600
Slim-line (C2) 3.125 5.000
Right side ranges
Constraint Lower limit Upper limit
Raw materials 316.667 No upper
limit
Packing boxes 200.000 320.000

Labour 75.000 90.000
Required:
(a) Formulate the above problem (6 marks)
(b) What is the optimal daily production plan? (2 marks)
(c) What is the maximum selling price for the standard model that will keep the
same optimal solution as in (b) above? (1
mark)
(d) Suppose C1 was changed from its current value to Sh. 5.50. Would the optimal
solution change? Why? (1
mark)
(e) Suppose C2 was changed from its current value to Sh. 4.00. Would the optimal
solution change? Why? (1
mark)
(f) Suppose simultaneously C1 changed to Sh. 5.50 and C2 changed to Sh. 4.00.
Would the optimal solution change? Why?
(2 marks)
(g) What is the shadow price for man-hours? Interpret. (2 marks)
(h) What is the shadow price of the packing? Interpret. (2 marks)
(i) Suppose simultaneously the amount of material available increased from 350 to
500 the number of boxes available increased from 300 to 310 and the number
of man-hours increased from 80 to 84. What conclusion can be drawn
regarding the shadow price? Why?
(3 marks)