The Colonial House Furniture Company manufactures four-drawer oak filing cabinet

Question

The Colonial House Furniture Company manufactures four-drawer oak filing cabinets in six stages. In the first stage, the boards forming the walls of the cabinet are cut; in the second stage, the front drawer panels are woodworked; in the third stage, the boards are sanded and finished; in the fourth stage, the boards are cleaned, stained, and painted with a clear finish; in the fifth stage, the hardware for pulls, runners, and fittings is installed; and in the final stage, the cabinets are assembled. Inspection occurs at each stage of the process, and the average percentages of good-quality units are as follows.

Stage

Average Percentage Good Quality

1

87%

2

91%

3

94%

4

93%

5

93%

6

96%

The cabinets are produced in weekly production runs with a product input for 300 units.

a.  

Determine the weekly product yield of good-quality cabinets.

b.  

What would weekly product input have to be in order to achieve a final weekly product yield of 300 cabinets?

Stage

Average Percentage Good Quality

1

87%

2

91%

3

94%

4

93%

5

93%

6

96%

Explanation / Answer

a. The formula to be used is: Yield = I*g1%*g2%*g3%*g4%*g5%*g6%

I = input and g1, g2,g3,g4,g5,g6% = good quality work in process at stages 1,2,3,4,5,6 respectively.

Thus weekly product yields of good quality cabinets = 300*87%*91%*94%*93%*93%*96%

= 185.37 cabinets or 185 cabinets (rounded off).

b. Now let the input be I. yield = 300.

Thus 300 = I*87%*91%*94%*93%*93%*96%

300 = I*0.617910576

or I = 300/0.617910576

or I = 485.5 cabinets or 486 cabinets (rounded off).

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