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Wilmington Chemical Company produces three products: ethylene, butane, and ester. Each of these products has high demand in the market, and Wilmington Chemical is able to sell as much as it can produce of all three. The reaction operation is a bottleneck in the process and is running at $100\%$ of capacity. Wilmington wants to improve chemical operation profitability. The variable conversion cost is $$10$ per process hour. The fixed cost is $$400,000.$ In addition, the cost analyst was able to determine the following information about the three products:

Ethylene Butane Ester

Budgeted units produced $9,0009,0009,000$

Total process hours per unit $4\mathrm{.}04\mathrm{.}03\mathrm{.}0$

Reactor hours per unit $1\mathrm{.}51\mathrm{.}00\mathrm{.}5$

Unit selling price $$170$ $$155$ $$130$

Direct materials cost per unit $$115$ $$88$ $$85$

The reaction operation is part of the total process for each of these three products. Thus, for example, $1\mathrm{.}5$ of the $4\mathrm{.}0$ hours required to process ethylene is associated with the reactor.

Required:

$1.$ Determine the unit contribution margin for each product.

Contribution Margin

Per Unit

Ethylene $fill in the blank $1$

Butane $fill in the blank $2$

Ester $fill in the blank $3$

$2.$ Provide an analysis to determine the relative product profitabilities, assuming that the reactor is a bottleneck.

Contribution Margin

Per Reactor Hour

Ethylene $fill in the blank $4$

Butane $fill in the blank $5$

Ester $fill in the blank $6$

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