Ajax Petroleum Company currently distills $500,000$ barrels of crude oil into $300,000$ barrels of kerosene and $200,000$ barrels of residual oil in its oil refinery each year. This transformation process is determined solely by the properties of the oil and cannot be adjusted by Ajax. The price of crude oil is $$64$ per barrel. Variable distillation costs are $$16$ per barrel. The fixed costs associated with the distillation portion of the refinery are $$28$ million per year. Of these fixed costs, $$16$ million is depreciation of the refinery and $$12$ million is the cash fixed costs. There are no costs incurred after the split$-$off point. Kerosene sells for $$200$ per barrel; residual oil sells for $$75$ per barrel.

Ajax uses the net realizable value method to allocate joint costs between kerosene and residual oil.

$($PLEASE SHOW STEPS$)$

QUESTION $1.$

What are the total joint costs that Ajax will allocate between kerosene and residual oil using the net realizable value method?

QUESTION $2.$

What percentage of the joint costs will be allocated to kerosene? Your answer should be a number between zero and $100.$

QUESTION $3.$

Suppose that Ajax is considering buying a catalytic cracking unit $($cat cracker$)$ that can refine up to $100,000$ barrels of the residual oil per year into home heating oil at a variable cost of $$12$ per barrel. The cat cracker will cost $$60$ million, last $30$ years, have no salvage value, and will be depreciated on a straight$-$line basis over $30$ years. What is the minimum price per barrel of home heating oil for which Ajax should buy the cat cracker?