Carlyle Lighting Products produces two different types of lamps: a floor lamp and a desk lamp.

Floor lamps sell for $$30$ and desk lamps sell for $$20.$

The projected income statement for the upcoming year follows:

Sales $$600,000$

Less: Variable costs $400,000$

Contribution margin $200,000$

Less: Fixed costs $150,000$

Operating income $$50,000$

The owner of Carlyle$$s estimates that $60$ percent of the sales revenues will be produced by floor lamps and the remaining $40$ percent by desk lamps.

Floor lamps are also responsible for $60$ percent of the variable expenses. Of the fixed expenses, one$-$third are common to both products, and one$-$half are directly traceable to the floor lamp product line.

Required:

$1.$ Compute the sales revenue that must be earned for Carlyle to break even.

$5$ Marks

$2.$ Compute the number of floor lamps and desk lamps that must be sold for Carlyle to break even.

$10$ Marks

$3.$ Compute the degree of operating leverage for Carlyle Lighting Products. Now assume that the actual revenues will be $40$ percent higher than the projected revenues.

$5$ Marks

$4.$ By what percentage will profits increase with this change in sales volume? What is the theory behind the operating leverage concept?

$5$ Marks