Fifth edition Alnoor Bhimani Charles T. Horngren Srikant M. Datar Madhav V. Rajan Farah Ahamed

Optimal production plan, computer manufacturer

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Trial Corner ( X ; Y ) Total contribution margin

10.15 Optimal production plan, computer manufacturer.
(30 min)
1
Let
X
= Units of printers, and Y = Units of desktop computers. Objective Maximise total contribution margin of €200X + €100Y Constraints For production line 1:
6X + 4Y < 24
For production line 2:
10X
< 20
Sales of
X
and Y:
X
− Y < 0
Negative production impossible:
X
> 0

Y
> 0
2
Solution Exhibit 10.15 presents a graphical summary of the relationships. The sales- mix constraint here is somewhat unusual. The X − Y < 0 line is the one going upward at 45° angle from the origin. Using the trial-and-error method:
Trial Corner
(X; Y)
Total contribution margin
1 2
3 4
(0; 0)
(2; 2)
(2; 3)
(0; 6)
€200 (0)
+
€100 (0)
=
€0 200 (2)
+
100 (2)
=
600 200 (2)
+
100 (3)
=
700 200 (0)
+
100 (6)
=
600 The optimal solution that maximises operating income is two printers and three computers.

Bhimani, Horngren, Datar and Rajan, Management and Cost Accounting, 5
th
Edition, Instructor’s Manual
© Pearson Education Limited 2012

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