The Cocoa Edibles Factory manufactures and distributes chocolate products. It purchases cocoa beans and processes them into two intermediate$$ products: chocolate$-$powder liquor base and$$ milk$-$chocolate liquor base. These two intermediate products become separately identifiable at a single splitoff point. Every $2$ comma $100$ pounds of cocoa beans yields $40$ gallons of$$ chocolate$-$powder liquor base and $60$ gallons of$$ milk$-$chocolate liquor base.

The$$ chocolate$-$powder liquor base is further processed into chocolate powder. Every $40$ gallons of$$ chocolate$-$powder liquor base yield $660$ pounds of chocolate powder. The$$ milk$-$chocolate liquor base is further processed into milk chocolate. Every $60$ gallons of$$ milk$-$chocolate liquor base yield $1,080$ pounds of milk chocolate. Production and sales data for August are as follows$($assume no beginning$$ inventory$)$: More info

times Cocoa beans$$ processed, $31$ comma $500$ pounds

times Costs of processing cocoa beans to splitoff point$($including purchase of$$ beans$),$ $ $66,000$

Production

Sales

Selling Price

Separable Processing Costs

Chocolate powder

$9,900$ pounds

$6,600$ pounds

$$10$ per pound

$$57,090$

Milk chocolate

$16,200$ pounds

$14,000$ pounds

$$11$ per pound

$$77,110$

Cocoa Edibles Factory fully processes both of its intermediate products into chocolate powder or milk chocolate. There is an active market for these intermediate products. In$$ August, Cocoa Edibles Factory could have sold the$$ chocolate$-$powder liquor base for $ $42$ a gallon and the$$ milk$-$chocolate liquor base for $ $52$ a gallon. Required

$1.$

Calculate how the joint costs of $ $66,000$ would be allocated between chocolate powder and milk chocolate under the following$$ methods:

a$.$

Sales value at splitoff

b$.$

Physical measure$($gallons$)$

c$.$

NRV$($Net Realizable$$ Value$)$

d$.$

Constant$$ gross$-$margin percentage NRV

$2.$

What are the$$ gross$-$margin percentages of chocolate powder and milk chocolate under each of the methods in requirement$1?$

$3.$

Could Cocoa Edibles Factory have increased its operating income by a change in its decision to fully process both of its intermediate$$ products? Show your computations.