Assignment-3 - assignment 3 PDF

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assignment 3...

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Faculty of Business and Information Technology

Assignment 3 Value: 5%, Due: Mar 21st @ 11:59 PM This assignment should be completed individually. We take academic integrity seriously. Any student found to be involved in plagiarism or cheating will be penalized in accordance to the Ontario Tech University Calendar Section 5.15. To assert that you have not given or received, or used unauthorized assistance, write the following pledge in the comment textbox when you submit your files through Blackboard system. "I have not given, received, or used any unauthorized assistance." Assignment Instruction: You must submit your detailed workout file in order to get the full mark on this assignment. Your assignment solution can be typed, scanned, or quality picture. However, if your solution is scanned or picture, YOU MUST PASTE THE SCANNED OR PICTURE DOCUMENTS ONTO ONE MS WORD/PDF FILE. NOTE: Any assignment without valid workout file will receive a grade of ZERO.

1. [12 Points] Summarize the pertinent information obtained by applying the graphing strategy

and sketch the graph of : 𝑓(𝑥) =

𝑥+9 𝑥−9

2. [13 Points] Summarize the pertinent information obtained by applying the graphing strategy

and sketch the graph of : 𝑓(𝑥) = ln(𝑥 2 + 36)

3. [15 Points] A T-shirt manufacturer is planning to expand its workforce. It estimates that the

number of T-shirts produced by hiring x new workers is given by 𝑇(𝑥) = −0.75𝑥 4 + 15𝑥 3 where 0 ≤ 𝑥 ≤ 15 When is the rate of change of T-shirt production increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate of change for T-shirt production? Graph T and T′ on the same coordinate system.

4. [16 Points] Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per

suit must be 𝑝= 180 − 0.75𝑥. It also determines that the total cost of producing x suits is given by 𝐶(𝑥) = 3000 + 0.5𝑥 2 a) Find the total revenue, 𝑅(𝑥) b) Find the total profit, 𝑃(𝑥) c) How many suits must the company produce and sell in order to maximize profit? d) What is the maximum profit? e) What price per suit must be charged in order to maximize profit? 5. [14 Points] According A car rental agency rents 480 cars per day at a rate of $30 per day. For

each $1 increase in rate, 10 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income? 6. [15 Points] A publishing company sells 400,000 copies of certain books each year. It costs the

company $1 to store each book for a year. Each time it must print additional copies, it costs the company $500 to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs? 7. [15 Points] A dairy is planning to introduce and promote a new line of organic ice cream. After

test marketing the new line in a large city, the marketing research department found that the demand in that city is given approximately by the following equation, where x thousand quarts were sold per week at a price of $𝑝 each, and whose revenue function is given as 𝑅(𝑥)=𝑥𝑝 𝑝= 15𝑒 −𝑥 , 0< 𝑥 < 5 (a) Find the local extrema for the revenue function. (b) On which intervals is the graph of the revenue function Concave upward? Concave downward?

Submission Guideline: Using Canvas system, please submit your solution file by no later than March 21st, 2021 at 11:59PM....