Mark Sanders Blog Post 3

Mark Sanders

11/4/14

Applied Calculus

Blog Post #3

Part One

The Red Coat Company is a company which produces coats in a variety of different red shades. The target demographic for the company is primarily made up of teenagers and young adults. The company has been around for about three decades and has established itself as a popular clothing/fashion brand amongst the teenage and young adult demographic. The company distributes coats all over the world with particularly strong markets in North America and Western Europe.

Part Two

Fixed costs for the company include the following:

Salaries: $250,000

Rent For Buildings and Factories: $200,000

Maintenance/Electricity: $150,000

Supplies: $200,000

Advertising: $300,000

Research/Development: $500,000

The cost for producing a single red coat is 20 dollars regardless of the color of coat. The Red Coat Company sells these coats for 50 dollars each.

The cost function is C(q)= 20q + 1,600,000.

The revenue function is R(q)= 50q.

The profit function is P(q)= 50(q)- (20q+1,600,000).

Breakeven Point

0=50q-20q-1,600,000

-30q=1,600,000

1,600,000/-30= 53333.3333

The breakeven point is 53,333.3333 coats. At this point, the company will make a profit.

The breakeven point is the number of coats that must be sold for The Red Coat Company to completely pay for all costs. On the graph, the breakeven point is represented by the black dot.  After this point, every coat sold will provide profit for the company. The slopes of the graphs represent the

amount of cost and revenue for any number of coats sold. It costs a significantly lower amount to produce a jacket then a jacket is sold for so the slope of the cost function is less steep than that of the revenue function. However, due to fixed costs, the graph of the cost function starts at $1,600,000 as opposed to $0 like the revenue function.

The profit function steadily increases as more coats are sold. The breakeven point (Black Dot), however, is at (53,333.3333, 1,600,000). Once the line passes zero on the y axis, the company is able to profit when selling that many coats.

Part Three

Each day, The Red Coat Company produces and sells 65,000 coats.

q= 65,000.

On the revenue and cost function graph, the total production per day is represented by red dots.

The marginal cost per unit produced is $20. At the 65,000th value, the marginal cost will be $20 for a new unit to be produced.

(20(65,000)+1,600,000)/65,000= 44.615

The average cost per unit when producing the 65,000 value is about $45.

Questions

1.      The marginal revenue is greater than the marginal cost. At 65,000 units produced and sold, the fixed and variable costs amount to less than that of the revenue thus allowing for a profit.

2.      The number of units is greater than (after) the breakeven point. This means that the company is making a profit as the total revenue is greater than the total costs.

3.       R(q+1)- R(q)

50(56,000+1)- 50(56,000)= 50

C(q+1)-C(q)

[20(56,000+1)+1,600,000]- [20(56,000)+ 1,600,000]= 20

50-20= 30

It is beneficial for the company to produce an additional unit for that any additional unit produced at this point will provide an additional $30 in profit for the company.

4.      At q=n, an increase in production will decrease the average cost as the fixed costs are quite great and therefore inflate the average cost when n is a relatively low number.

5.      Decreasing the average costs would be better for the company. As average costs fall, profit will increase for each unit sold. This would allow The Red Coat Company to grow their profit and invest additional money back into the company.

Part Four

The Red Coat Company is very profitable and will therefore have additional funds to invest back into the company. With profits of $350,000 a day, The Red Coat Company has a large return on its production of coats. These funds can be used to advertise or develop new products. The company should, therefore, do very well over the next five years as revenue and profits are strong. In addition, the company is old and has an established name. This aspect of the company will keep the company from seeing sales decline too quickly as many consumers trust and recognize the company. If The Red Coat Company uses its profits to invest back into the company, the company may be able to grow sales and profits in the near future.