CHILD'S PLAY COMPANY $($A$)$ Child's Play Company makes a plastic rattle for toddlers. The rattle is generally marketed through exclusive retailers located in upscale shopping malls. The company used $23$ retailers. In late $2023,$ Diana Suares, the president of the company, was considering alternative marketing plans presented to her by Bill Dings, the marketing manager. Based on sales from January through October $2023,$ Diana expected that $2024$ sales would amount to $300,000$ units at $$8\mathrm{.}00$ per unit. Diana Suares also had with her some cost data for $2023$ supplied by the CFO, Don Capp. Don expects that these costs are reliable estimates for a volume up to $400,000$ units. Beyond $400,000$ units, the company would have to rent additional machines $($with a capacity of $100,000$ units each$)$ at an annual cost of $$50,000$ per machine $($in $2023).$ The data are presented in Exhibit A$.$ Total fixed manufacturing and selling and administrative costs are each expected to increase in $2024$ by $10$ percent because of inflation. Variable costs per unit and the selling price would stay the same as in $2023.$

Exhibit A $(2023$ Cost Data$)$ Manufacturing costs for rattles $($based on production volume of $300,000$ units$).$

Direct material $$0\mathrm{.}80$ per unit $*$

Direct labor $$10$ per hour $*($Each worker can make $20$ units in an hour$)$ Packaging $$0\mathrm{.}75$ per unit $*$

Power, supplies, indirect labor, and other variable production costs $$1\mathrm{.}20$ per unit$*$ Supervisory salaries, equipment rental, and miscellaneous production costs $$1\mathrm{.}80$ per unit

$*$ These costs vary in total with production volume

Selling and administrative costs $($based on sales volume of $300,000$ units$).$

Commissions to sales staff $10\%$ of price to retailer $**$

Shipping $$0\mathrm{.}50$ per unit $**$

Advertising and promotion $$0\mathrm{.}60$ per unit

Administrative staff salaries, depreciation on office equipment, etc $$0\mathrm{.}90$ per unit

$**$ These costs vary in total with sales volume.

For $2024$:

$1.$ What is the materials cost at $300,000$ units?

$2.$ What is the materials cost at $400,000$ units?

$3.$ What is the total variable cost at $200,000$ units?

$4.$ What is the total variable cost at $400,000$ units?

$5.$ What is the fixed manufacturing cost at $300,000$ units?

$6.$ What is the fixed manufacturing cost at $400,000$ units?

$7.$ What is the fixed manufacturing cost at $450,000$ units?

$8.$ What is the total fixed cost at $300,000$ units?

$9.$ What is the total fixed cost at $400,000$ units?

$10.$ What is the contribution margin per unit?

$11.$ What is the contribution margin if $1000$ units are sold?

$12.$ What is the contribution margin if $100,000$ units are sold?

$13.$ What is the profit at the break even volume?

$14.$ What is the contribution margin at the break even volume?

$15.$ What is the break even volume?

$16.$ What is the profit at $1000$ units above break even?

$17.$ What is the profit at $2000$ units below the break even?

$18.$ What is the profit at $100,000$ units above break even?

$19.$ What is the margin of safety at $1000$ units above break even?

$20.$ What is the sales volume required to give $$100,000$ profit before tax? $21.$ What is the sales volume required to give $$180,000$ after tax? Assume a tax rate of $40\%.$