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 quantity for each machine, we need to determine the quantity at which the cost is equal to the revenue. In this case, the cost function is given by the equations a), b), and c), and the revenue function is given by the demand function p(x) = -4x + 42.5.
To find the break-even quantity, we set the cost function equal to the revenue function and solve for x.
a) For machine a with the cost function f(x) = 4.1x + 92.16, we set f(x) equal to p(x):
4.1x + 92.16 = -4x + 42.5
To solve for x, we will need to rearrange the equation:
4.1x + 4x = 42.5 - 92.16
8.1x = -49.66
x = -49.66 / 8.1
x ≈ -6.13
Since quantities cannot be negative in this context, we can ignore the negative value. Therefore, the break-even quantity for machine a is approximately 6.13 thousand units.
b) For machine b with the cost function f(x) = 17.9x + 19.36, we set f(x) equal to p(x):
17.9x + 19.36 = -4x + 42.5
Rearranging the equation:
17.9x + 4x = 42.5 - 19.36
21.9x = 23.14
x = 23.14 / 21.9
x ≈ 1.06
The break-even quantity for machine b is approximately 1.06 thousand units.
c) For machine c with the cost function f(x) = 8.8x + 55.4, we set f(x) equal to p(x):
8.8x + 55.4 = -4x + 42.5
Rearranging the equation:
8.8x + 4x = 42.5 - 55.4
12.8x = -12.9
x = -12.9 / 12.8
x ≈ -1.01
Again, we need to ignore the negative value as it doesn't make sense in this context. Therefore, the break-even quantity for machine c is approximately 1.01 thousand units.
So, the break-even quantities for the three machines are approximately:
a) 6.13 thousand units
b) 1.06 thousand units
c) 1.01 thousand units