JTME-001135 – MATHEMATICS AND STATISTICS FOR BUSINESS AND SOCIAL SCIENCES – TAKE HOME EXAM
MATHEMATICS代写 DUE IN: Sunday, 19.05.2019 at 23.59,HOW: electronically in pdf-format via submission to www.turnitin.comClass id: 21073370
JACOBS UNIVERSITY BREMEN
DUE IN: Sunday, 19.05.2019 at 23.59,
HOW: electronically in pdf-format via submission to www.turnitin.com
Class id: 21073370MATHEMATICS代写
enrollment password:: MS20fBSS19
Please register for the class on turnitin ahead of time.
GROUP WORK: is allowed with a maximum of 2 persons per group.MATHEMATICS代写
HOW MANY : There will be a total of two take home assignments in this semester. FORMAT: Please do the required analyses and provide answers in complete sentences. Use R to create graphs and to do computations. Include the R commands in your submission. Integrate requested figures or tables into your document and give a brief verbal comment/caption on them.
I herewith state that I have not received any unauthorized assistance in solving this exam.
(1)Apetito provides a college meal-service plan. Apetito has fixed costs of 450 000e perterm and variable costs of 375e per Apetito charges 900e per student per term. How many students must sign up with the Apetito plan in order for the company to make a profit?
(2)Youdrive at a constant speed from Bremen to Berlin, a distance of 400 About 170 kilometers from Bremen you pass through Braunschweig (Brunswick). Sketch a graph of your distance from Braunschweig (Brunswick) as a function of time.
(3)Acompany has cost function C(q) = 5000 + 4q dollars and revenue function R(q) = 20q dollars.MATHEMATICS代写
(a)Whatare the fixed costs for the company?
(b)What is the marginalcost?
(c)Whatprice is the company charging for its product?
(d)Graph C(q) and R(q) on the same axes and label the break-even point, q0. Explainhow you know the company makes a profit if the quantity produced is greater than q0.
(e)Find the break-even pointq0.
(4)Anew bus worth 200 000e in 2019 depreciates linearly to 20,000e in 2035.MATHEMATICS代写
(a)Finda formula for the value of the bus, V , as a function of time, t, in years since 2019.
(b)What is the value of the bus in2025?MATHEMATICS代写
(c)Find and interpret the vertical and horizontal intercepts of the graph of the function.
(d)Whatis the domain of the function?
(5)Acement company asked for your advice regarding their production They own two production sites. MATHEMATICS代写
Site I has a maximum cement production capacity of 20 tons per hour while Site II has a maximum production capacity of 30 tons per hour. The production at Site I produces 2.5 tons of CO2 emissions per ton of cement produced while Site II produces only 1 ton of CO2 emissions per ton of cement produced. According to regulations the company is allowed to emit a maximum of 70 tons of CO2 emissions per hour.MATHEMATICS代写
(a)The cement produced at Site I can be sold for a net profit of $20 per ton and thecement produced at Site II can be sold for a net profit of $30 per How much cement should be produced at each sites to maximize the profit?
(b)Aftersome more thorough analysis with your associate you realize that the real profit function is not You came up with two different functions to describe it (x = number of tons of cement produced per hour at Site I and y = number of tons of cement produced per hour at Site II):
(i) P (x, y) = −x2 − y2 + 46x + 54yMATHEMATICS代写
(ii) P (x, y) = −x2 − y2 + 26x + 46y
For each of these functions determine how much cement should be produced at each sites to maximize the profit?MATHEMATICS代写
(c)Federalregulations allow companies to exceed the limit on CO2 emissions if they pay extra fine. Should you advise this company to purchase those certificates that allow the higher emission limits if the cost of them is $3 per ton of CO2? Answer the question for each of the three different profit (Hint: in- vestigate the net profit after paying the fine for those critical points and corner points that were outside of the region due to the original emission limits)
(6)The standard 52-card deck of French playing cards is the most common deck of playingcards used It includes thirteen ranks in each of the four French suits: clubs, diamonds, hearts, and spades. Each suit includes an ace, a king, a queen and a jack, and ranks two through ten. Cards with an ace, a king, a queen or a jack are called face cards.
(a)Computethe probability of drawing a red card or an ace on a single draw from a well-shuffled MATHEMATICS代写
(b)Prove that red and ace are independent events in a standard deck of cards.
(c)Provethat ace and face card are mutually exclusive events.
(d)Provethat ace and face card are not independent events.
(7)A random variable X has the triangular pdf
(a)PlotfX(x) for a suitable range of x.
(b)Find the cdf,FX(x).
(c)PlotFX(x) for a suitable range of x.
(d)Markthe region defined by the left hand side of the following equations in one of the above plots (whichever is more suitable). Then indicate which of the following statements are true or false and provide justifification.MATHEMATICS代写
(i) P (X 0.4) = 0.36
(ii) P (X y/2) = y2, for any 0 ley 1
(iii) P (0.6 X 0.9) = 0.3
(iv) The upper quartile of the distribution of X is 0.5.
(8)Fora continuous random variable X write each of the following probabilities in two different ways, one in terms of fX(x) and one in terms of FX(x):
(a) P (X > 10)
(b) P (5 < X < 10)
(c) P (5 < X < 10orX > 50).MATHEMATICS代写
(9)There are twelve cars crossing a bridge per minute on average. Which probability distribution would you assume for this situation? Find the probability of having seventeenor more cars crossing the bridge in a particular minute (use R to solve)!