a) f(x) = 4.1x +92.16
b) f(x) = 17.9x + 19.36
c) f(x) = 8.8x + 55.4
ANSWERS: a) 4.8 b) 0.93 c) 2.2, i just have no clue how they got these answers
EXTRA INFO:
The demand function for a new product is p(x)= - 4x +42.5, where x is the quantity sold in thousands and p is the price in dollars. the company that manufactures the product is planning to buy a new machine for the plant. there are 3 diff. types of machines. the cost function for each machine is shown (ABOVE). Investigate the break even quantities for each machine.
To find the break-even quantities for each machine, we need to determine the value of x when the cost of manufacturing equals the revenue generated from selling the product.
The cost function for each machine is given by the equations:
a) f(x) = 4.1x + 92.16
b) f(x) = 17.9x + 19.36
c) f(x) = 8.8x + 55.4
To find the break-even quantity, we set the cost function equal to the demand function (revenue function) and solve for x.
For machine a), we set the cost function equal to the demand function:
4.1x + 92.16 = -4x + 42.5
Now, let's solve this equation:
4.1x + 4x = 42.5 - 92.16
8.1x = -49.66
x = -49.66 / 8.1
x ≈ -6.13
Since x represents the quantity sold, it cannot be negative in this case. Therefore, it doesn't make sense to have a negative break-even quantity. This means that machine a) does not have a break-even quantity in a practical sense.
Similarly, we can find the break-even quantity for machine b):
17.9x + 19.36 = -4x + 42.5
Let's solve this equation:
17.9x + 4x = 42.5 - 19.36
21.9x = 23.14
x = 23.14 / 21.9
x ≈ 1.056
Therefore, the break-even quantity for machine b) is approximately 1.056 thousand units.
Finally, let's find the break-even quantity for machine c):
8.8x + 55.4 = -4x + 42.5
Simplifying the equation:
8.8x + 4x = 42.5 - 55.4
12.8x = -12.9
x = -12.9 / 12.8
x ≈ -1.008
Similar to machine a), having a negative break-even quantity doesn't make sense in this scenario. So, machine c) also does not have a practical break-even quantity.
In summary, the break-even quantity for machine b) is approximately 1.056 thousand units. Machines a) and c) do not have a practical break-even quantity.