EX $7-29($Algo$)$ Retail; CVP Analysis with Multiple Products $($LO $7-1,7-2,7-5)$

Tim$$s Bicycle Shop sells $21-$speed bicycles. For purposes of a cost$-$volume$-$profit analysis, the shop owner has divided sales into two categories, as follows:

Product TypeSales PriceInvoice CostSales CommissionHigh$-$quality$ $1,850$$ $840$$ $100$Medium$-$quality$92062040$

Three$-$quarters of the shop$$s sales are medium$-$quality bikes. The shop$$s annual fixed expenses are $$270,400.($In the following requirements, ignore income taxes.$)$

Required:

Compute the unit contribution margin for each product type.

What is the shop$$s sales mix?

Compute the weighted$-$average unit contribution margin, assuming a constant sales mix.

What is the shop$$s break$-$even sales volume in dollars? Assume a constant sales mix.

How many bicycles of each type must be sold to earn a target net income of $$126,750?$ Assume a constant sales mix.