The Bean Company provides fresh coffee beans for restaurants, hotels, and other food service companies. Bean offers three types of coffee beans: Premium, Gourmet, and Quality. Each of the three coffees is produced in a joint process in which beans are cleaned and sorted. The sorting process is the split$-$off point in this joint process, and the output is the three types of beans. The beans can be sold at the split$-$off point or processed further, with different types of roasting and additional sorting. The additional processing requires additional, separable processing costs, as shown next. Separable processing requires no special facilities, and the production costs of further processing are entirely variable and traceable to the products involved. Last year all three products were processed beyond split$-$off. Joint production costs for the year were $$160,000,000.$ Sales values and costs needed to evaluate Bean$$s production policy follow:

Premium Gourmet Quality Total

Pounds produced $24,000,00038,800,0004,800,00067,600,000$

Separable processing cost $ $23,000,000$ $ $21,000,000$ $ $19,000,000$ $ $63,000,000$

Pounds sold $24,000,00038,800,0004,800,00067,600,000$

Total joint cost $ $160,000,000$

Sales price$/$pound $($after additional processing$)$ $$53$ $$1$

Sales price at split$-$off $321$

Required:

$1.$ Determine last year$$s unit cost and unit gross profit for each product assuming Bean allocates joint production costs using the physical measure method.

$2.$ Determine unit cost and unit gross profit for each product if Bean allocates joint costs using the sales value at split$-$off method.

$3.$ Which of Bean$$s products should be processed further?