Choosing most profitable production volume. Answer the following questions.

Blanchard Company manufactures and sells dresses at a variable cost of $$30$ each and a fixed cost of x$.$ It can sell $6,000$ dresses at a selling price of $$50$ to earn an operating income of $$20,000$ or it can sell $3,500$ dresses at a selling price of $$60$ and another $2,000$ dresses at a selling price of $$40.$ Which alternative should Blanchard choose?

Canta Corporation manufactures and sells a special kind of ball bearing. Its cost structure depends on the number of bearings it produces. Its fixed costs and variable manufacturing cost per unit for different ranges of production are described in the following table:

Production Range in Units Fixed Costs Variable Manufacturing Cost per Unit

$13,000$ $$250,000$ $$75$

$3,0016000$ $$350,000$ $$50$

$6,00110,000$ $$750,000$ $$25$

Canta$$s sales director believes the company can sell $2,500$ units at a selling price of $$300$; or $5,000$ units at a price of $$200$; or $8,000$ units at a price of $$175.$ If it chose to sell $8,000$ units, however, it would incur additional advertising costs of $$50,000$ and variable selling costs of $$5$ per unit.

Should Canta Corporation plan to produce and sell $($a$)2,500$ units $($b$)5,000$ units or $($c$)8,000$ units?

Required

$3-31$ Operating leverage. Cover Rugs is holding a $2-$week carpet sale at Josh$$s Club, a local warehouse store. Cover Rugs plans to sell carpets for $$950$ each. The company will purchase the carpets from a local distributor for $$760$ each, with the privilege of returning any unsold units for a full refund. Josh$$s Club has offered Cover Rugs two payment alternatives for the use of space.

Option $1$: A fixed payment of $$7,410$ for the sale period

Option $2$: $10\%$ of total revenues earned during the sale period

Assume Cover Rugs will incur no other costs.

Calculate the breakeven point in units for $($a$)$ Option $1$ and $($b$)$ Option $2.$

At what level of revenues will Cover Rugs earn the same operating income under either option?

For what range of unit sales will Cover Rugs prefer Option $1?$

For what range of unit sales will Cover Rugs prefer Option $2?$

Calculate the degree of operating leverage at sales of $65$ units for the two rental options.

Briefly explain and interpret your answer to requirement $3.$