Assume Converse, a Nike company, plans to expand its manufacturing capacity to allow up to $48,000$ pairs of a new shoe product each year. Because only one product can be produced, management is deciding between the production of the Roadrunner for backpacking and the Trail Runner for exercising. A marketing analysis indicates Converse could sell between $19,200$ and $32,000$ pairs of either product.

The accounting department has developed the following price and cost information:

Product

Roadrunner

Product:

Trail

Runner

Selling price per pair

$$140$

$$125$

Variable costs per pair

$80$

$75$

Fixed production costs

$$240,000$

$$160,000$

The accounting department has developed the following price and cost information:

Additional annual facility costs, regardless of product, are estimated at $$160,000$Assume Converse is subject to a $20\%$income tax rate.

Required

a$).$Determine the number of pairs of each product that Converse must sell to obtain an aftertax profit of $$80,000$

Note: Round your answer up to the nearest whole unit for example, round $41\mathrm{.}2$to $42$

Roadrunner: $\_\_\_\_\_\_\_\_\_\_$pairs

Trail Runner:$\_\_\_\_\_\_\_\_\_\_\_\_\_$pairs

b$).$Determine the number of pairs of each product Converse must sell to obtain identical beforetax profit.

Note: Round your answer up to the nearest whole unit for example, round $41\mathrm{.}2$to $42$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$pairs of each type

c$).$For the solution to requirement $($b$)$calculate Converse's aftertax profit or loss.

Roadrunner: $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Trail Runner: $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

d$).$Which product should Converse produce if both products were guaranteed to sell at least $28,800$pairs$?$

e$).$How much would the variable costs per pair of the product not selected in requirement d $$have to fall before both products provide the same profit at sales of $28,800$pairs$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$$CVP Analysis of Alternative Products

Converse could sell between $19,200$ and $32,000$ pairs of either product

The accounting department has developed the following price and cost information:

Required

a$.$ Determine the number of pairs of each product that Converse must sell to obtain an after$-$tax profit of $$80,000.$

Note: Round your answer up to the nearest whole unit $($for example, round $41\mathrm{.}2$ to $42).$

Roadrunner: $$

pairs

Trail Runner: $$

pairs

b$.$ Determine the number of pairs of each product Converse must sell to obtain identical before$-$tax profit.

Note: Round your answer up to the nearest whole unit $($for example, round $41\mathrm{.}2$ to $42).$

pairs of each type

c$.$ For the solution to requirement $($b$),$ calculate Converse's after$-$tax profit or loss.

Roadrunner: :

Trail Runner: $$0$

d$.$ Which product should Converse produce if both products were guaranteed to sell at least $28,800$ pairs?

e$.$ How much would the variable costs per pair of the product not selected in requirement $($d$)$ have to fall before both products provide the same profit at sales of $28,800$ pairs?