A company makes women's shoes. The price of the duty-free sale of a pair of shoes
is set at 180 €. The total production cost C (x), in euros, is expressed as a function of the number x of
pairs of shoes sold by:
C x () = + 1.5 1 x x5 +1350 2 with x ∈ [] 10; 80
c. In an orthogonal coordinate system having a unit of 1 cm for 10 pairs of shoes on the abscissa and 500 €
for 2 cm on the y-axis, represent function B set to [] 10; 80.
d. Graphically determine the solutions of equation B (x) = 3000.
your text is all messed up, so hard to say.
There are lots of online graphing sites though, so use one of them.
To graphically represent function B, we need to plot points on the coordinate system. The given function is C(x) = 1.5x^2 + 1350.
1. Determine the range of x-values from the given interval [10, 80]. These x-values will be marked on the x-axis of the coordinate system.
2. Calculate the corresponding y-values for each x-value by substituting the value of x into the function. This will give us the cost C(x) for each pair of shoes sold.
3. Scale the x-axis and y-axis according to the given units. Since 10 pairs of shoes correspond to 1 cm and 500 € correspond to 2 cm, we can label the x-axis with increments of 1 cm for every 10 pairs of shoes and the y-axis with increments of 2 cm for every 500 €.
4. Plot the points on the coordinate system using the scaled x and y values.
5. Connect the points with a smooth curve to represent function B.
Now, let's move on to determining the solutions of equation B(x) = 3000 graphically:
1. Draw a horizontal line representing y = 3000 on the coordinate system.
2. Find the intersections between the line and the curve representing function B. These points of intersection will represent the x-values where B(x) equals 3000.
3. Mark and label the x-coordinate of each point of intersection, as those will be the solutions of the equation B(x) = 3000.
By following these steps, you can accurately represent function B on the coordinate system and determine the solutions to equation B(x) = 3000.