A firm uses activity-based costing. Its activity rates are as follows. $100 per machine hours, $500 per batch start, $5 per order The firm produces several products. Two of these products have the following data

Product 1: $44,000 revenue, $10,000 direct costs, 50 machine hours, 5 batch starts, 100 orders
Product 2: $46,000 revenue, $20,000 direct costs, 20 machine hours, 8 batch starts, 200 orders
The firm's product sales mix is 3:1 for product 1 and 2, respectively

Which of these re-mixes is LEAST profitable to the firm? (Assume the same number of bundles would be sold.)
(A) The firm's new product sales mix is 4:0 for product 1 and 2, respectively
(B) The firm's new product sales mix is 0:4 for product 1 and 2, respectively
(C) The firm's new product sales mix is 1:3 for product 1 and 2, respectively
(D) The firm's product sales mix stays at 3:1 for product 1 and 2, respectively (i.e. the current product sales mix)

Hi, we have to find the income received by both products and then find the return on sales to see which mix perform the worst. To do this, we need to find the tariffs for the direct costs, machine ours, batch starts and orders.

For Product 1 is as follows

Price= Revenue/Orders = 44,000/100= $440/order

Direct Costs = 10,000/100 =$100/order

Machine Hours = (50/100)*$100 = $50/order

Batch Starts = (5/100)*500= $25

Order = $5 (and that is it)

So you are making an income of:

Income/order= $440 - $100 - $50 - $25 - $5 =$260

That is: Return on sales = 260/440= 59.09%

Now, let´s do Product 2

Price= Revenue/Orders = 46,000/200= $230/order

Direct Costs = 20,000/200 =$100/order

Machine Hours = (20/200)*$100 = $10/order

Batch Starts = (8/200)*500= $20

Order = $5 (and that is it)

So you are making an income of:

Income/order= $230 - $100 - $10 - $20 - $5 =$95

That is: Return on sales = 95/230= 41.30%

So the more you sell of product 1, the best, or, in other words, the more you sell of product 2 the worse your revenue will perform. This is why you will perform the worst if you go for option B), which is the less profitable option.

Attached to this answer I am leaving you an excel sheet based on 1,000 orders to convince you.

Best of luck.