Two automatic systems for dispensing maps are being compared by the state highway department. The accompanying breakeven chart o
f the compar- ison of these systems (System I vs. System IT) shows 2-16 total yearly costs for the number of maps dispensed per year for both alternatives. Answer the following questions.
(a) What is the fixed cost for System I?
(b) What is the fixed cost for System II?
(c) What is the variable cost per map dispensed for System I?
(d) What is the variable cost per map dispensed for System 11?
(e) What is the breakeven point in terms of maps dispensed at which the two systems have equal annual costs?
(a) What is the fixed cost for System I?
(b) What is the fixed cost for System II?
(c) What is the variable cost per map dispensed for System I?
(d) What is the variable cost per map dispensed for System 11?
(e) What is the breakeven point in terms of maps dispensed at which the two systems have equal annual costs?
1 answer:
Full question attached
Answer:
A. $1000
B. $5000
C. $0.9
D. $0.10
E. 5 maps
Explanation:
A. From the diagram in the question, we can see the equation of the cost, the constant to the right of the equation is the fixed cost
B. The same is applicable as in question A
C. The variable cost can be seen in the equation where we observe the cost per map- 0.9 per unit X
D. Same is applicable as in question C
E. The break-even point is 5 maps as seen in diagram in question. At this point both equations equal $5500
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Answer:
1. That values that you must plot are:
- (1, 4.08))
- (20, 5.08)
- (40, 6.18)
2. Yes, the plot of those three points is straight enough.
Explanation:
<em><u>A. What are the values you will plot? </u></em>
The x-ccordinate of your plot is still the number of years the exmployees have worked for the company.
The y-coordinate of your plot is the the base-10 logarithm of the salary.
Therefore:
<u>1) A part-time shipping clerk</u>: 1 year, $12,000
⇒
<u>2) A manager</u>: 20 years, $120,000
⇒
<u>3) The CEO</u>: 40 years ago, $1,500,000
⇒
Summarizing, the points to plot are:
- (1, 4.08)
- (20, 5.08)
- (40, 6.18)
<u><em>B. Will the plot of these three points be straight enough?</em></u>
To find whether the plot is straight enoguh, you may either plot them, make a regression, or, since they are only three points, you can whether the change of rate of the points is constant.
- <u>Change of rate of the first two points, r</u>:
r = rise/run = Δy / Δx = (5.08 - 4.08) / (20 - 1) =1.00/19 ≈ 0.05
- <u>Change of rate of the second and the third points, r</u>:
r = rise/run = Δy / Δx = (6.18 - 5.08) / (20 - 1) = 0.05
Since both rate of changes are equal (or reasonably equal) the plot is straight enough.