Explain why the vertical line test is used to determine if a graph represent a function
2 answers:
Vertical line test tells us whether the graph represents a function or not. This test states that "if a vertical line intersects the graph at only one point then it is a function otherwise not"
Now, if any vertical line intersects the graph at two points then it means that for a value of x, we have to y values. In other words the x value has not unique y values which doesn't satisfy the condition of a relation to be a function.
Therefore, if the vertical line intersects the graph at only point then only each x values has a unique y values.
Please see the attached images. Image 1 is not a function since the vertical line intersects at two points whereas, image 2 represents a function.
Hence, we can conclude that vertical line test is used to determine if a graph represent a function.
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Answer:
a. 21 327 hot dogs/run
b. 70 runs/yr
c. 4 da/run
Step-by-step explanation:
Data:
Production rate (p) = 5000/da
Usage rate (u) = 260/da
Setup cost (S) = $66
Annual carrying cost (H) = $0.45/hot dog
Production days (d) = 294 da
Calculations:
a. Optimal run size
(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)
= 1 470 000 hot dogs/yr
(ii) Economic run size
= 21 327 hot dogs/run
b. Number of runs per year
Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)
= 70 runs/yr
c. Length of a run
Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)
= 4 da/run