1. If you can sell a product for $67 and it costs you $28 per unit to produce, w

Question

1. If you can sell a product for $67 and it costs you $28 per unit to produce, while also paying $3,900 per month in fixed expenses, how many units must you sell each month in order to earn a monthly profit of $2,500? Show all your work.

2. Using the information from the first problem, your variable costs per unit include labor ($18) and parts ($10). Your fixed costs include maintenance of $750, rent and utilities of $2000, and administration costs of $1150. If you have a labor issue and your costs might vary by $2 next month; and you might have a major repair issue that will add $500; and your administrative costs might vary by 10%. Which is the most important issue to focus on? Conduct a sensitivity analysis of the situation and show all of your work.

Explanation / Answer

1.

Let x units must you sell each month in order to earn a monthly profit of $2,500

So total cost for x unit per months = variable cost + fixed cost

C(x) = 28x + 3900

if you can sell a product for $67

so revenue function R(x) = 67x

therefore Profit function P(x) = Revenue - Cost

P(x) = 28x +3900 - 46x

P(x) = -13x + 3900

Now to have profit 2500

ie P(x) = 2500

so -13x +3900 = 2500

13x = 3900-2500

x = 1400/13

x = 107.69

so he must sell 107 unit to have profit of $2500

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