Ronald Roth started his new job as controller with Aerosystems today. Carole, the employee benefits clerk, gave Ronald a packet that contains Information on the company's health insurance options. Aerosystems offers its employees the choice between a private insurance company plan (Blue Cross/Blue Shield), an HMO, and a PPO. Ronald needs to review the packet and make a decision on which health care program fits his needs. The following is an overview of that information. a) The monthly premium cost to Ronald for the Blue Cross/Blue Shield plan will be $60.82, For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 30 percent and the insurance company will cover 70 percent of covered charges. The annual deductible is $630. b) The HMO is provided to employees free of charge. The copayment for doctors' office visits and major medical charges is $10 Prescription copayments are $5. The HMO pays 100 percent after Ronald's copayment. There is no annual deductible. c) The POS requires that the employee pay $43.01 per month to supplement the cost of the program with the company's payment If Ron uses health care providers within the plan, he pays the copayments as described above for the HMO with no annual deductible. He can also choose to use a healthcare provider out of the network and pay 30 percent of all charges after he pays a $630 deductible. The POS will pay for 70 percent of those covered visits. Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician three times during the year at a cost of $210 for each visit. He also spent $83 and $107 on two prescriptions during the year. What total costs will Ronald pay if he enrolls in the HMO plan? Personal annual costQuestion 2. Use undetermined coefficients to solve the following initial value problem: 1' + 2y'ty = 20-1 y(0) = 1 y'(0) = 0Question 18. Given that the eigenvalues of the matrix A = A = 2, -1, with corresponding eigenvectors K = . 4 . what is the general solution of the following system of differential equations? de = 30 - y du = Ar - 2y (a) x = ge"+me', y = qe" + 4cge"' (b) x = ate, y = a+40 (c) x = qell, y = get (d) x =e" tel, y= e# + 4e-+ Question 19. Let /(2) = \\x|, -T [on cos (nor) + on sin(nr)] 1= 1 be its Fourier series. Which of the following statements is true? (a) do = 0. (b) an = 0 for n = 1, 2,3, .... (c) by = 0 for n = 1, 2,3, .... (d) Both (a) and (b). Question 20. The partial differential equation Her + Hyy = 0 is called Laplace's equation. Which of the following functions is a product solution of Laplace's equation? (a) u(x,y) =2-y (b) u(x,y) = et sin(y) (c) u(x,y) = zy (d) All of the above.Question 7. Given that what is the solution of the following system of linear equations? x + 2y - = = 2 2rty+z = 1 - y+2: =-1 (a) r = 0, y = 1, = =0. (b) The system has no solution. (c) x = -t, y = 1+t, = = 1 (t arbitrary). (d) x = -t, y = 1+t, = =0 (t arbitrary). Question 8. Let y1 = et and ys = tell. Which of the following statements is true about W(y , 92), the Wronshian of y and yz? (a) W(31,92) = ell, therefore y and yz are linearly independent. (b) W(1. 92) = e", therefore y and yz are linearly dependent. (c) W(y1,92) = 0, therefore in and y2 are linearly independent. (d) W(1,92) =0, therefore th and yz are linearly dependent. Question 9. Consider the 2nd-order non-homogeneous differential equation y" - 41 + 3y =e'+12. What is the complementary ( or homogeneous) solution? (a) ye = cie' + cat? (b) ye = cie-'+ cge-31 (c) ye = cie' + cget (d) ye = cie' + eye-30 Question 10. For the differential equation in the previous question, what is the correct form for a particular solution? (a) Up = Ae' + B12 (b) Up = Ae' + B12 + Ci + D (c) Up = Ate' + Biz (d) Up = Ate' + B12 + Ci + DQuestion 6. A 1 kg mass is attached to a spring with constant 13 N/ m. The system is immersed in a medium which offers a damping force numerically equal to 6 times the instantaneous velocity. If x is the displacement of the mass from equilibrium, measured in meters, then " + 67 + 131 = 0. Which of the following statements is true? (a) r(t) = gett + ages, and the system is underdamped. (b) r(t) = get+ gerst, and the system is overdamped. (e) r(t) = qe-3 cos(21 ) + cge-3 sin(21), and the system is underdamped. (d) r(t) = ge-3 cos(21 ) + cge-3 sin( 21), and the system is overdamped.11. The analysis of the transfer oriented firm suggests that the firm will locate at the input source or the market (a) Under what conditions could intermediate location compete with the input source or the market (b) What prevents (a) from occurring? 12. The principle of median location can be employed to analyze the locational decisions of transfer oriented firms with several input sources and markets. Answer the following. (a) Define the median transport location (b) What assumptions are necessary for the principle of median location to apply? (c) Why does the median transport location minimize transportation costs? 13. Using the principle of median location, explain why some industrial firms locate in trans- shipment points. 14. Labor oriented firms locate in cities and regions with low labor cost per unit of output (a) What are the two variables that affect labor cost per unit of output and how are they each related to labor cost? (b) Explain 4 reasons for spatial variation of labor costs. (c) Explain how amenities affect locational decisions of labor oriented firms. 15. In the post WWII era, many firms switched from transfer orientation to local input orientation. Describe the transportation and production innovations that produced this result. Give examples. 16. Cities attempt to attract firms by offering them subsidies. Explain 4 types of inducements. 17. According to the empirical studies, what effect do state and local taxes and public services have on location choices?Question 11. The Laplace transform of the function f(1) = (t + 2) is: (@) (# + ?)2 (b) 3 + ; (0) 3+ #+4 (d) Is+2) Question 12. The Laplace transform of the function /(1) = tsin(t) is: (a) (641) (b) -(8+1) (e ) + 1 (d) - 8241 1 Question 13. The inverse Laplace transform of the function -2" g F ( s ) = = 2+4 is : (a) } sin(21 - 4) U(t - 2) (b) cos(21 - 2) U(t - 2) (e) cos(21 - 4) U(t - 2) (d) 6(t - 2) cos(21) Question 14. Which of the following statements is true about t * t, the convolution of t with t? (a) 1 * 1 = for (1 -T)dT. (b) [{txt ) = 4. (c) txt = 6. (d) All of the above.4. (12 points) Bargaining. Consider the following variation on the alternating offers bargaining model. Three players bargain over how to divide a pie of size 1 among themselves. An offer of division has the form (3:1, :32, :63) where 3:1 + x2 + x3 = 1 and 3:, denotes player 's share of the pie. In period 1, player 1 makes an offer of division. Player 2 decides whether to accept or reject the o'er. If the offer is accepted by player 2, the game ends and the pie is split according to 1's offer. If player 2 rejects, the game proceeds to period 2. In period 2, player 2 makes an offer of division. Player 3 decides whether to accept or reject the offer. If the offer is accepted by player 3, the game ends and the pie is split according to 2'5 offer. If the offer is rejected, the game proceeds to period 3. In period 3, player 3 makes an offer of division. Player 1 decides whether to accept or reject the offer. If the offer is accepted by player 1, the game ends and the pie is Split according to 3'5 offer If the offer is rejected, the game ends and each player receives 0. Assume that when a player is indifferent between accepting and rejecting, the player accepts. Let 6 denote the players' common discount factor. Is there a subgame perfect Nash equilibrium in which an offer is accepted at period 1? If yes, construct one. If no, explain