Problem:

Mop and Broom Manufacturing is evaluating whether to produce a new type of mop. The company is considering the operations requirements for the mop as well as the market potential. Estimates of fixed costs per year are $40,000, and the variable cost for each mop produced is $20.

Required:

Question 1) If the company sells at a price of $25, how many units of product have to be sold in order to break even? [algebraic approach only]

Question 2) If the company sells 10,000 mops at the product price of $25, what will be the contribution to profit?

Question 3) Suppose the company has only managed to sell 20% less than the break-even quantity calculated in (a). The marketing department has advised not to raise the selling price to offset the loss due to the highly competitive demand market. Thus, the management has no other options but to lower its variable cost by finding less expensive raw materials. Assuming the fixed cost stays constant, calculate the new variable cost/unit of product at which the company will break even with respect to the new sales quantity.

Solve the given numerical problem and illustrate step by step calculation.