Question Consider a market in which the demand curve is given by Q = 28 - 2P. The supply curve is given by P = 2. The government is considering imposing a tax. If the government wants to maximize the tax revenue collected from this market, the optimal tax rate would be [Answer] per unit. (In decimal numbers, with two decimal places, please.)

Canadian currency today is credit money. deposit money. convertible paper money. commodity money. fiat money.

WWW 4. [10 marks] Consider the vector field F(x, y, z) = (3ye bye.1-sin ) and the curve C represented by F(t) = {x,y, 4) = (t,t +1, ita) from (0,1,0) to (2, 3, 46). (a) Determine F. dr by setting up the appropriate line integral, simplifying it, and then evaluating it. (The work of evaluating the integral need not be included.) (b) Clearly, F(x, y, ) is defined on all of R and each of its components has continuous partial derivatives. Using this information and the curl F, manually show that F(x, y, z) is conservative in Rs. (c) Determine a potential function (2, y, z) such that f=F. 34² ex Ex (2,4, 2) = 3y²ex - f/1.9, 2) = yee & #(9,2). (d) Using the Fundamental Theorem for Line Integrals, manually verify the result in part (a). Grade: 27

QUESTION THREE (15 MARKS) A laboratory process receives medical samples from hospitals in its area and then subjects them to a number of tests that take place in different parts of the laboratory. The average response time for the laboratory to complete all its tests and mail the results back to the hospital (measured from the time that the sample for analysis arrives) is three days. A recent process map has shown that, of the 60 minutes that is needed to complete all the tests, the tests themselves took 30 minutes, moving the samples between each test area took 10 min- utes, and double checking the results took a further 20 minutes. What is the throughput effi- ciency of this process? What is the value-added throughput efficiency of the process? (State any assumptions that you are making.) If the process is rearranged so that all the tests are performed in the same area, thus eliminating the time to move between test areas, and the tests themselves are improved to half the amount of time needed for double checking, what effect would this have on the value-added throughput efficiency? QUESTION FOUR (15 MARKS) The regional government office that deals with passport applications is designing a process that will check applications and issue the documents. The number of applications to be processed is 1,600 per week and the time available to process the applications is 40 hours per week. (a) What is the required cycle time for the process? (b) If the total work content of all the activities that make up the total task of checking, processing and issuing a passport is, on average, 30 minutes, how many people will be needed to meet demand? (c) The passport office has a 'clear desk policy that means that all desks must be clear of work by the end of the day. How many applications should be loaded onto the process in the morning in order to ensure that every one is completed and desks are clear by the end of the day? (Assume a working day of 7.5 hours (450 minutes).)

Let \( \sum_{k=1}^{\infty} a_{k} \) be a series with \( n \)th partial sum \( S_{n}=1-\frac{n}{2 n+4} \). Find each of the following. Make sure to fully justify your answers (no need to simplify fractions). (a) \( a_{1} \) (b) \( \sum_{k=1}^{\infty} a_{k} \) (c) \( \lim _{k \rightarrow \infty} a_{k} \) (d) \( \sum_{k=101}^{200} a_{k} \) (e) \( a_{100} \) Let k=1∑∞​ak​ be a series with nth partial sum Sn​=1−2n+4n​. Find each of the following. Make sure to fully justify your answers (no need to simplify fractions). (a) a1​ (b) k=1∑∞​ak​ (c) k→∞lim​ak​ (d) k=101∑200​ak​ (e) a100​

12. Company MN a wholesale distributor. It uses an ABC system to analyze customer profitability for its small and medium-sized retail customers. The cost pool cost driver and other relevant information is shown below Small retailer Costs 300.000 Medium retailer 4.000 8.000 Cost pool Ordering Delivery Customer Service Total overhead Cost driver Number of orders Number of deliveries Number of products sold 4.200 750,000 1.200.000 10.000 320,000 480,000 2.250.000 What is the average tatal.overhead costret.product sold to medium retailer? (Avsuming every item sold requires certain involvement of customer service 53.81 550.00 125.00 12.15

Two long straight wires carrying conventional current I are connected by a three-quarter-circular arc of radius R (see the figure). (The rest of the circuit is far enough away that it contributes little magnetic field in this region.) Electric fields are also present in this region, due to charges not shown on the drawing. An electron is moving to the right with speed v as it passes through the center C of the arc, and at that instant the net electric and magnetic force on the electron is zero. Part 3 If the current is 7 A, the radius of the loop is 0.034 m, and the speed of the electron is 6.7 × 105 m/s: (c) What is the magnitude of the magnetic field at the center C, due to the current I? |B⇀|= T Part 4 (d) What is the magnitude of the electric field at the center C? |E⇀|= N/C Radius R 1 C. Electron 14