Task 3

Calculate a formula for P and draw the graph in a coordinate system.

To determine the demand function p(x), where the price in DKK units at a demand of x pcs. we can use the data that was collected back in 2019. When the price was reduced from DKK 1500 per PCS. down to DKK 1300 per pcs., where the demand increased from 50 pcs. to 70 pcs. per week this means that we use two points (x1, y1) and (x2, y2), where x1 and x2 are the quantity sold and p1 and p2 are the prices at the points.

X1 = 50, p1 = 1500 X2 = 70, p2 = 1300

We start by calculating the slope (a) using the formula for the slope between these two points: a=(y2 - y1)/(x2-x1)

a=(1300-1500)/(70-50)-10

After calculating the slope (x), we can use the point and a to find b by plugging the values into the demand function formula p(x) = ax + b.

1500 = - 10 * 50 + b

1500 = -500 + b

b = 2000

demand function is therefore: -10x + 2000

P(x) is here the price in DKK per pcs., and x is the demand in number of pcs. The graph of this function will be a straight line with a negative slope of -10, and y-intercept of 2000. The graph in this exercise is a straight line with a negative slope, as it represents the price in DKK per PCS. as a function of the demand in number of pieces. in this case it has been observed that when the price has been lowered from DKK 1500 per PCS. to DKK 1300 per PCS. increased demand from 50 pcs. for 50 pcs. per week. A straight line with a negative slope means that there is an inverse relationship between the price of a product and the quantity that people want to buy ie. when the price falls, there are more people who want to buy the product, and when the price rises, there are more people who buy the product. This method is typically used to prove how price affects demand in the economy. Price and demand move in opposite directions, when price goes down, demand moves up, and vice versa.

Determine a regulation for R.

The total variable costs of producing and selling the GPS model could in 2019 be described by a function C with the regulation c(x)=13/72x^3-25x^2+1850x The function above shows how the total variable costs change in relation to the demand (x) for GPS models. It is a third-degree polynomial function with three terms, each term having a specific influence on the total cost. R(x) = P(x) * x

(-10+2000) * 2000x - 10 x^2

= 2000x - 10x^2

Draw the graphs of R and C in the same coordinate system.

The company wanted to determine the optimal price of CARMINE. When you draw both functions in the same coordinate system, we get two curves. The interesting point to look at is the point where the curves intersect, as it is the point that shows us where revenue and costs are equal. This point can either be called the balance point or what is called the break-even point. The point is important for the company as it indicates how many units the company must sell in order to cover the costs.

Here is the graph of both the revenue (R) and the total variable costs (C) in the same coordinate system:

Determine the offset where the tangents to the graphs of the two functions have the same slope.

The total contribution margin can be determined as the difference between the turnover and the total variable costs, i.e. The total contribution margin = the turnover - the total variable costs

To find the point where the tangents to the graphs of revenue (R) and total variable costs (C) have the same slope, we need to find the place where the two graphs are equally steep. This point is going to represent the amount of GPS units that need to be sold to cover the cost with the revenue.

When using the CAS tool, one can calculate the tangents to the graph by using two derived prescriptions. We start by deriving the function c(x)=13/72 x^3-25x^2+1850x and then the function R(x) = - 10x^2+2000x

C`(x) = 13/24 x^2-50x+1850 R`(x) = -20x + 2000

(-20x + 2000 = 13/24 x^2-50x+1850)

x = - 60/13 , x = 60

Show that the largest possible coverage contribution is DKK 24,000 per week.

In order to be able to prove that the largest possible coverage contribution is DKK 24,000 per week you have to find the point where the difference between the income (R) and the costs (c) is greatest. The item will show the largest contribution to the profit. If the largest contribution to the profit is DKK 24,000, this means that the company can cover all costs and have a profit of DKK 24,000 per week.

DB(60) = 2400

By inserting 60 in x's place in the total coverage contribution function, you get the largest possible coverage contribution of DKK 24,000.

Determine the price that provides the largest contribution margin.

calculate the missing answers and correct the answers that are wrong