What will the profit be if 1500 units are sold next year?

In summary, the company experienced a loss of $5000 in its first year of operation due to having $15,000 tied up in fixed costs and spending $40,000 on raw materials and labor while only selling 500 units of their product. It is anticipated that next year, with an increase in sales to 1500 units at the same selling price, the company will turn a profit. The profit function is represented by P(p,x)=px-(80x+15000) where p is the price per unit and x is the number of units sold. By solving for p, the profit for selling 1500 units can be determined without the need for charts or tables.
  • #1
Simon T
16
0
the first year of operation for a small company yielded a loss of \$5000. The company has \$15,000 per year tied up in fixed costs and spent 40,000 on raw materials and labour. Since the company was not well known, they were only able to sell 500 units of their product that year. It is hoped that business with improve next year and that 1500 units will be sold at the same selling price as last year.

a) If 1500 units are sold next year, what will the profit be?
 
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  • #2
Profit is revenue less costs. There is a fixed cost of 15000 and a marginal cost of 80...if we denote the price of each unit as $p$ and the number of units sold as $x$, then our profit function $P$ is:

\(\displaystyle P(p,x)=px-\left(80x+15000\right)=(p-80)x-15000\)

Now, we are given:

\(\displaystyle P(p,500)=(p-80)500-15000=-5000\)

So, what is $p$?
 
  • #3
I was taught a different way for this module. I was taught to have a chart with Unit basis and total amount at the top and on the left side we have s, vc, cm, fc, and np and we fill in the numbers.
 
  • #4
Well, you're in for a treat then, as I'm going to help you answer this question in a much easier and more straightforward manner using a little algebra. (Yes)

Once you find $p$, then you will have the profit function in one variable $x$, into which you can simply plug the given value of $x$ to output the profit for that production level. No time consuming charts, graphs and/or tables required. (Bow)
 

FAQ: What will the profit be if 1500 units are sold next year?

What is break even analysis?

Break even analysis is a financial calculation that determines the point at which a company's total revenue equals its total costs. It helps businesses understand the minimum level of sales they need to cover their expenses and start generating profit.

Why is break even analysis important?

Break even analysis is important because it helps businesses make informed decisions about pricing, production levels, and sales strategies. It also allows them to identify potential risks and evaluate the financial feasibility of a project or product.

What are the components of break even analysis?

The components of break even analysis include fixed costs, variable costs, and sales price. Fixed costs refer to expenses that do not change with the level of production, such as rent and salaries. Variable costs are expenses that vary with the level of production, such as raw materials and labor. Sales price is the amount at which a product or service is sold.

How is break even analysis calculated?

Break even analysis is calculated by dividing the total fixed costs by the difference between the sales price and the variable cost per unit. The resulting number represents the number of units that need to be sold to break even. This can also be calculated in terms of sales revenue, by dividing the total fixed costs by the contribution margin (sales price - variable cost per unit).

What are the limitations of break even analysis?

Break even analysis assumes that all units produced are sold, and it does not take into account factors such as changes in demand, competition, and market trends. It also assumes that fixed costs and variable costs remain constant, which may not always be the case. Additionally, break even analysis is only accurate if all costs and revenues can be accurately identified and measured.

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