Domain is the set of the values of x (produced units) that are feasible. Which is all the positive integer values and zero.
Range is the set of possible results for c(x), i.e. possible costs.
You can substitute some values for x to help you, for example:
x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + 0.345 (4) = 187.38
3 200 - 21 + 0.345(9) = 182.105
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
So the function starts at c(x) = 200, decreases until the vertex (x =10, c=164.5) and then starts to increase.
Also, the range goes to 164.5 to infinity, limited to the solution for x = positive integers.
Answer:
This is a quadratic function, which is usually defined on all reals. But, the domain is restricted to X equal to or greater than 0 because it does not make sense to produce a negative number of units.
Find the vertex of the parabola at
(10.14, 164.5).
Since the parabola opens up, the range is Y equal to or greater than 164.5.
Step-by-step explanation:
