Solved where marginal revenue meets a $2.90 per-rider cost, the MT445 Unit 4 problem reaches 6,940 tickets at $31.12, then recommends a smaller step to $28. Searches like "mt 445 unit 4 assignment example", "mt445 unit 4 sample" and "mt445 unit 4 example" land here.
What a finished MT445 Unit 4 marginal analysis problem looks like
Four pages laid out as a numbered problem in five parts, each with given values, working and a one-line answer. Part one takes the Unit 3 regression at shoulder-week conditions, season three, no event and average rain, which reduces it to weekly tickets equal to 14,593 minus 245.9 times the fare. Part two inverts that equation and derives marginal revenue. Part three sets marginal cost at $2.90 a round trip, harbor fees on both legs plus card processing, and explains why vessel fuel and crew stay out of it. Part four solves: 6,940 tickets, a $31.12 fare and weekly contribution of $195,840 against $189,396 at today's $26. Part five pivots the demand line through today's point at each end of the coefficient's interval, where the best fare runs from $26.71 to $40.50.
How a MT445 Unit 4 example is structured
Marginal cost is defined before anything is solved, because the answer depends on what counts as the cost of one more rider, and a ferry with empty seats makes that figure unusually small. Once the schedule is set, fuel and crew are spent whether a sailing carries 90 riders or 390, so only per-rider charges vary. Algebra is shown line by line, ending with the check that marginal revenue equals $2.90 at the solution. A capacity test follows, since the shoulder schedule offers 10,500 round-trip seats a week and the solution needs 6,940, so constant cost holds. Peak weeks are flagged as a different problem, where seats run out. The interval section carries the most judgment: rather than trusting $31.12, a fare no rider has ever paid, the paper tests $28 against both ends and finds a worst case near minus $393.
Demand at shoulder-week conditions
With season three, no event and 2.11 rain days held fixed, the estimated equation becomes 14,593 minus 245.9 times the fare. The paper explains why peak and event weeks are left out of this calculation.
Marginal revenue, derived
Inverting gives a fare of 59.35 minus tickets divided by 245.9, so marginal revenue falls twice as fast: 59.35 minus twice the tickets over 245.9. Each step of the rearrangement is written out.
What one more rider costs
Harbor fees on both legs and card processing total $2.90 a round trip. Fuel and crew are committed once the schedule is fixed, so the problem leaves them out and says why in a sentence.
The solution and a capacity check
Setting marginal revenue to $2.90 yields 6,940 tickets and a $31.12 fare, with contribution about $6,444 a week higher. Demand sits well inside the 10,500 seats the shoulder schedule offers each week.
A fare nobody has paid
Pivoting the line through today's $26 point at the interval's ends puts the best fare between $26.71 and $40.50. A move to $28 gains $4,052 a week at the estimate and risks about $393 at worst.
Where marks go in MT445 Unit 4
Marginal cost is where this unit's papers most often go wrong, usually by dividing a week's vessel costs by riders and calling the result the cost of one more passenger. That average, about $5.40 a ticket here, nearly doubles the relevant figure and moves the answer for the wrong reason. A capacity check is expected too: an answer assuming constant cost past the point where sailings sell out is solving a different problem. Papers that verify marginal revenue at the solution guard against inversion slips. Presenting $31.12 as the recommendation, without noting that it sits above any fare in the data, draws comment in a good share of sections. Credit concentrates where the estimate's uncertainty reaches the decision and turns a point answer into a fare the line can defend.
Get a MT445 Unit 4 example written to your instructions
The Unit 4 problem as posted, or just its demand and cost functions, will do; add the rubric and whatever method your instructor demonstrated. Expect the worked sample in 24-48h, marginal cost defined before solving, algebra shown in full, and the answer tested against capacity and uncertainty. First requests carry no charge.
MT445 Unit 4 questions, answered
Why is marginal cost so low for a ferry passenger?
Because most costs are fixed once the sailing schedule is set. The boat burns about the same fuel and pays the same crew whether it carries 90 people or 390, so one more rider adds only charges that scale with riders, such as harbor fees and card processing. That changes when sailings fill, which is why your answer should state whether capacity binds.
Should the recommendation use the exact profit-maximizing price?
Report it, then judge it. If the calculated price lies outside the range the data cover, or the demand estimate is imprecise, a smaller step with a stated test is usually easier to defend. Show what the step earns at the estimate and at the ends of the interval, so the grader sees a recommendation that survives the uncertainty rather than ignoring it.
What if my problem supplies revenue and cost functions instead of a regression?
Then differentiate each to get marginal revenue and marginal cost, set them equal, solve for output, and substitute back for price. The reasoning is identical; only the starting point differs. Confirm that profit falls on either side of your answer, or check the second-order condition, and state any capacity limit the problem mentions.