Ozark Metal Company makes a single product that sells for $$43\mathrm{.}5$ per unit. Variable costs are $$26\mathrm{.}3$ per unit, and fixed costs total $$65,590$ per month.

Required:

a$.$ Calculate the number of units that must be sold each month for the firm to break even.

b$.$ Assume current sales are $$413,000.$ Calculate the margin of safety and the margin of safety ratio.

c$.$ Calculate operating income if $6,700$ units are sold in a month.

d$.$ Calculate operating income if the selling price is raised to $$46\mathrm{.}5$ per unit, advertising expenditures are increased by $$7,000$ per month, and monthly unit sales volume becomes $7,300$ units.

e$.$ Assume that the firm adds another product to its product line and that the new product sells for $$24$ per unit, has variable costs of $$15$ per unit, and causes fixed expenses in total to increase to $$82,000$ per month. Calculate the firm's operating income if $6,700$ units of the original product and $4,500$ units of the new product are sold each month. For the original product, use the selling price and variable cost data given in the problem statement.

f$.$ Calculate the firm's operating income if $4,600$ units of the original product and $6,600$ units of the new product are sold each month.

g$.$ Why operating income is different in parts $e$ and $f,$ even though sales totaled $11,200$ units in each case.