Question Q-1. Explain each of the following statements using supply-and-demand diagrams.a. “When a cold snap hits Florida, the price of orange juice rises in supermarkets throughout the country.”b. “When the weather turns warm in New England every summer, the price of hotel rooms in Caribbean resorts plummets.”c. “When a war breaks out in the Middle East, the price of gasoline rises and the price of a used Cadillac falls.”

Part 1 (2 points) See Hint Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p = 38.00 - Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production: (Round to two decimals if necessary.) Firm 2 production: (Round to two decimals if necessary.) Part 2 (2 points) See Hint What are the profits for each firm in equilibrium? Firm 1 profit: $ (Round to two decimals if necessary.) Firm 2 profit: $ (Round to two decimals if necessary.)

Assume that you measured the length of an object as 50 mm using a digital caliber. The measurement was made at 300 + 5 K. What is the actual measurement result? (Resolution of the digital caliber: 0.04 mm, coverage factor: 3, linear thermal expansion coefficients of the digital caliber and the sample are 14*10-6 KP)

Determine the reactions at the supports A and C. The frame is pin connected at A, B, and C and the two joints are fixed connected. SKN 6 kN 10 kN/m 2 kN/m B 4 m A 3 m -2 m -1 m -

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Vout(s) . You may assume that the capacitor and inductor are initially de- Vin(s) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t)). Find the time response Vout(t) = [-{Vout(s)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for vout (t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) All corner frequencies iii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3 H 000m 0.25 12 Vin(t) 0.2F 112 Vout(t) Figure 2: System for Question 3

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Your C). You may assume that the capacitor and inductor are initially de- Vin) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t) ). Find the time response Vout(t) = [-!{Vout($)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for Vout(t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) ii. All corner frequencies ii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3H 000 0.252 Vin(t) 0.2F 11 Vout(t) Figure 2: System for Question 3

the worst case. 4: Show that there are at most [n/2h+1] nodes of height h in an n-element heap