$1.$ Break$-$even analysisTo be profitable, a firm must recover its costs. These costs include both its fixed and its variable costs. One way that a firm evaluates at what stage it would recover the invested costs is to calculate how many units or how much in dollar sales is necessary for the firm to earn a profit.Consider the case of Blue Mouse Manufacturers:Blue Mouse Manufacturers is considering a project that will have fixed costs of $$10,000,000.$ The product will be sold for $$32\mathrm{.}50$ per unit, and will incur a variable cost of $$10\mathrm{.}75$ per unit.Given Blue Mouses cost structure, it will have to sell$$units to break even on this project $($QBE$).$Blue Mouse Manufacturerss marketing sales director doesnt think that the market for the firms goods is big enough to sell enough units to make the companys target operating profit of $$15,000,000.$ In fact, she believes that the firm will be able to sell only about $200,000$ units. However, she also thinks the demand for Blue Mouse Manufacturerss product is relatively inelastic, so the firm can increase the sale price. Assuming that the firm can sell $200,000$ units, what price must it set to meet the CFOs EBIT goal of $$15,000,000?$$$156\mathrm{.}11$ per unit$$169\mathrm{.}69$ per unit$$135\mathrm{.}75$ per unit$$142\mathrm{.}54$ per unitWhat affects the firms operating break$-$even point?Several factors affect a firms operating break$-$even point. Based on the scenarios described in the following table, indicate whether these factors would increase, decrease, or leave unchanged a firms break$-$even quantityassuming that only the listed factor changes and all other relevant factors remain constant.IncreaseDecreaseNo ChangeThe firms tax rate increases.The variable cost per unit decreases.The firm depreciates its fixed assets more quickly over a shorter life.When a large percentage of a firms costs are fixed, the firm is said to have a$$degree of operating leverage.