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This is just a simple equal allocation of the joint costs between the two products. The costs should have been allocated using NRV.
This answer includes all of the whey that was produced. The demand for the whey is only 375 pounds, not the full 450 pounds that are produced. Only the whey that will be sold should be included since the selling price of the units that are not sold will be $0.
This answer did not include the overhead in the calculation of the common costs to allocate.
The NRV of an item is calculated as the selling price minus the costs to complete and dispose. In this question there are no further processing costs, so we will use the sales price at the splitoff as the NRV; so even though the problem specifies NRV, we are actually using the Relative Sales Value (or Gross Market Value) method. In order to allocate the joint costs, we need to calculate the total sales value that all of the joint products have at the splitoff point. One pound of cheese has a sales price of $2 and there were 450 pounds produced (see "Output"), so this is a sales value of $900. One pound of whey has a sales price of $.80 and there will be only 375 pounds of whey that will be able to be sold 1, so this is $300 (the whey that will not be sold will bring no sales value to the company since the sales price is $0). The total sales value is thus $900 + $300, or $1,200. The cheese accounts for 75% of it ($900 ÷ $1,200). This means that the cheese will get 75% of the common costs. The whey accounts for 25% ($300 ÷ $1,200), so the whey will get 25% of the common costs. Now we need to calculate the common costs to be allocated. They are made up of $200 of milk, $400 of labor and $400 of overhead. This is $1,000 and 75% of it is $750 for the cheese. The other 25% or $250 will go to the whey. 1We are often asked why the allocation of costs for the whey is based on its demand and not on the amount produced. The answer is because the whey is a secondary product, or byproduct, and only 375 pounds of whey will ever be able to be sold. That does not mean the other 75 pounds will sit in inventory and be sold eventually. It means the other 75 pounds will never be sold and will have to be disposed of. Therefore, we cannot assign any cost to those 75 unsellable pounds, because they will never bring any revenue to the company. If the company were to allocate some cost to those 75 pounds and put them into Inventory, it would only end up writing their value down to zero and taking a loss later. So instead, the company allocates the cost to the 375 pounds that will be sold.