fraha Chemicals produces three chemical products, Alpha, Beta and Omega. Raw materials
are processed in a single plant to produce two intermediate products, Sigma and Iota, in fixed
proportions. There is no market for these two intermediate products. Sigma is processed
further through process X to yield the product Alpha, product Iota in converted into Beta by a
2
separate finishing process Y. The Y finishing process produces both Beta and a waste material,
Theta, which has no market value. The company can convert Theta, after additional processing
through process Z, into a saleable by-product, Omega. Afraha Chemicals can sell as much
Omega as it can produce at a price of Ksh. 1.50 per kg.
At normal levels of production and sales, 600,000 kg of common input material are processed
each month. There are 440,000 kg and 110,000 kg respectively, of the intermediate products
Sigma and Iota, produced from this level of input. After separate finishing processes, fixed
proportions of Alpha, Beta and Omega emerge, as shown below with current market prices (all
losses are normal losses):
Product Quantity Market price per kg
Ksh
Alpha 400,000 2.425
Beta 100,000 4.50
Omega 10,000 1.50
At these normal volumes, materials and processing costs are as follows:
Common plant Separate finishing
Facility processes
X Y Z
‘000’ ‘000’ ‘000’ ‘000’
Direct materials 320 110 15 1.0
Direct labour 150 225 90 5.5
Variable overhead 30 50 25 0.5
Fixed overhead 50 25 5 3.0
Total 550 410 135 10.0
Selling and administrative costs are entirely fixed and cannot be traced to any of the three
products.

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