? Rare Earth, Inc. produces two batteries $-$ ?high capacity and low capacity. Management would like to know the optimal sales mix based on the following data:

?

?$1)$ ?Raw materials consist of casings and lithium ion cells.

?$2)$ ?Lithium$-$ion cells cost $$50$ ?each.

?$3)$ ?There are $30$ ?cells in the HighCap battery and only $12$ ?in the LowCap.

?$4)$ ?The casings for the LowCap cost $$500$ ?each; the casings for the HighCap cost $$800$ ?each.

?

It takes $25$ ?hours of direct labor to assemble a HighCap and $20$ ?hours to assemble a LowCap. The standard labor rate is $$40$ ?per hour.

?

The main constraint on production is the size of the facility, which is $8,000$ ?square feet, of which $6,000$ ?is dedicated to HighCap production and $2,000$ ?to LowCap. The company prefers to manufacture HighCap because it is used in Teslas and other high$-$profile cars.

?

Fixed costs are currently as follows:

?

Fixed costs per month Total

Sales Salary $$12,000$ ?

Selling, General, and Administrative $$90,000$ ?

Production facility rent $$10,000$ ?

?$$112,000$ ?

?

The company currently sells $60$ ?HighCap batteries and $100$ ?LowCap batteries per month. HighCap batteries sell for $$8,000$ ?each, and LowCap batteries sell for $$4,000.$ ?

?

$1.$ ?Create a current contribution margin income statement with allocated fixed costs. Allocate Sales Salary and SG&A using units sold, and Production Facility Rent using square footage.

?

Production facility HighCap LowCap Total

Square feet

Allocation rate

?

?HighCap LowCap Total

Current Sales Volume

Allocation rate

?

Variable Costs per unit HighCap LowCap

Casings

Lithium$-$Ion cells

Labor per assembled battery

?

?

Fixed costs per month HighCap LowCap Total

Sales Salary allocated based on units sold

Selling, General, and Administrative allocated based on units sold

Production facility rent allocated based on square footage

?

?

Rare Earth, Inc.

Product Mix

CVP Analysis $($month$)$ ?

?

?HighCap LowCap Total

Sales

Variable costs

Contribution Margin

Fixed costs

Operating income

?

?

$2.$ ?How many units of HighCap could the company produce if it shifted all production space to that product line?

a$.$ ?

Current production space square feet

Current production units

Production space per unit

b$.$ ?

Total production space square feet

Production space per unit

Total capacity units

?

?

$3.$ ?How many units of LowCap could the company produce if it shifted all production space to that product line?

a$.$ ?

Current production space square feet

Current production units

Production space per unit

b$.$ ?

Total production space square feet

Production space per unit

Total capacity units

?

$4.$ ?Calculate the contribution margin per unit for the constraint $($production facility space$)$:

?HighCap LowCap

Units produced

Square feet of space

Units produced per SF

Contribution margin$/$unit

Contribution margin$/$SF

Capacity

Total CM at Capacity

?

$5.$ ?Create a contribution margin income statement for Rare Earth, Inc. if it shifts all of its production to LowCap, assuming there is enough market demand to absorb the extra production:

?

Rare Earth, Inc.

Product Mix

CVP Analysis $($month$)$ ?

Units $0400$ ?

?HighCap LowCap Total

Sales

Variable costs

Contribution Margin

Fixed costs

Operating incomeRare Earth, Inc. produces two batteries $-$ ?high capacity and low capacity. Management would like to know the optimal sales mix

based on the following data:

Raw materials consist of casings and lithium ion cells.

Lithium$-$ion cells cost $$50$ ?each.

There are $30$ ?cells in the HiqhCap battery and only $12$ ?in the LowCap.

The casings for the LowCap cost $$500$ ?each; the casings for the HiqhCap cost $$800$ ?eact

It takes $25$ ?hours of direct labor to assemble a HighCap and $20$ ?hours to assemble a LowCap. The standard labor rate is $$40$ ?per

hour.

The main constraint on production is the size of the Facility, which is $8,000$ ?square feet, of which $6,000$ ?is dedicated to HighCap

production and $2,000$ ?to LowCap. The company prefers to manufacture HighCap because it is used in Teslas and other high$-$

profile cars.

Fined costs are currently as follows:

The company currently sells $60$ ?HighCap batteries and $100$ ?LowCap batteries per month. HighCap batteries sell for $$8,000$ ?each,

and LowCap batteries sell for $$4,000.$

Create a current contribution margin income statement with allocated fised costs. Al