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PR $7-51($Algo$)$ Cost$-$Volume$-$Profit Analysis with Income Taxes and Multiple Products $($Appendix$)($LO $7-1,7-2,7-4,7-5,7-11)$

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Alpine Thrills Ski Company recently expanded its manufacturing capacity. The firm will now be able to produce up to $16,000$ pairs of cross$-$country skis of either the mountaineering model or the touring model. The sales department assures management that it can sell between $10,000$ and $14,000$ units of either product this year. Because the models are very similar, the company will produce only one of the two models.

The following information was compiled by the accounting department.

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Model

Mountaineering

Touring

Selling price per unit

$ $133\mathrm{.}00$

$ $121\mathrm{.}00$

Variable costs per unit

$79\mathrm{.}70$

$79\mathrm{.}70$

Fixed costs will total $$558,400$ if the mountaineering model is produced but will be only $$478,200$ if the touring model is produced. Alpine Thrills Ski Company is subject to a $30$ percent income tax rate.

PR $7-51($Algo$)$ Part $1$: Compute the contribution$-$margin ratio for the touring model.

Required:

$2.$If Alpine Thrills Ski Company desires an after$-$tax net income of $$33,620,$ how many pairs of touring skis will the company have to sell?

Note: Enter your answer as a decimal rounded to two places.