Jane is planning to expand her business by taking on a new product. She can purchase the new product at a cost of $2 per unit. To market this new product, she would need to spend $1250 on advertising each month. She is not sure how she should price her product and is asking for your help. If she chooses a price of $14.5 per unit, what will be the break-even point in sales dollars? Note: to receive the full mark, you will use 8 decimal places when performing the calculations, and there is no need to put dollar sign ($) or comma (,) in your final answer. You may leave 8 decimals in your final answer if you wish to do so.

Question

BlackTom AI · Accepted Answer

We start by identifying the key financial numbers involved in the problem. The fixed monthly advertising cost is 1250, which does not change with the number of units sold. The variable cost per unit to produce the product is 2 dollars. The selling price per unit is 14.5 dollars.

Next, we determine the contribution per unit, which is the amount each unit contributes toward covering fixed costs and profit after variable costs are paid. Contribution per unit = price per unit - variable cost per unit = 14.5 - 2 = 12.5.

To reach the break-even point in units, we divide the total fixed costs by the contribution per unit: break-even units = fixed costs / contribution per unit = 1250 / 12.5 = 100.00000000 units. Here we keep the calculation with exact arithmetic, which yields exactly 100 units.

Finally, we convert the break-even units into sales dollars by multiplying by the selling price per unit: break-even sales dollars = break-even units * price per unit = 100.00000000 * 14.5 = 1450.00000000.

Therefore, the break-even point in sales dollars, staying consistent with eight decimal places, is 1450.00000000. (Note: the problem allows leaving eight decimals, and there is no need to include a dollar sign or comma in the final numeric answer.)

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