CVP and Sensitivity Analysis $($Single Product$).$ Madera Company has annual fixed costs totaling $$120,000$ and variable costs of $$3$ per unit. Each unit of product is sold for $$15.$ Madera expects to sell $12,000$ units this year $($this is the base case$).$

Required:

Find the break$-$even point in units.

How many units must be sold to earn an annual profit of $$50,000?($Round to the nearest unit.$)$

Find the break$-$even point in sales dollars.

What amount of sales dollars is required to earn an annual profit of $$70,000?$

Find the margin of safety in units and in sales dollars.

Prepare a contribution margin income statement for the base case.

What will the operating profit $($loss$)$ be if the sales price decreases $30$ percent? $($Assume total sales remains at $12,000$ units, and round to the nearest cent where appropriate.$)$

Go back to the base case. What will the operating profit $($loss$)$ be if the variable cost per unit increases $10$ percent? $($Assume total sales remains at $12,000$ units, and round to the nearest cent where appropriate.$)$