Page 392 - PM Integrated Workbook 2018-19

Chapter 15

Example 2, continued

Department A time is a critical constraint with no slack. Calculate the shadow
price for one additional hour of department A’s time.

The optimal solution (x = 625, y = 600) was found where the department A
and Product Y constraints crossed. Optimum corner is corner C, the
intersection of

8x + 10y = 11,000 and y = 600

At this corner, x = 625 and y = 600

With one additional hour of department A time, the new set of equations is

8x + 10y = 11,001 (1)

y = 600 (2)

We then multiply (2) by 10:

10 y = 6,000 (3)

We then subtract (3) from (2)

8x = 5,001

So x = (5,001/8)

x = 625.125

To calculate a revised optimal contribution C

C = (625.125 × $4) + (600 × $8) = $7,300.5

Compared to the original contribution of $7,300, this is an increase of $0.50

The shadow price per hour in Department A is therefore $0.50.

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