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Instructions: The submission for this HW include a single PDF file, in addition to code files containing solutions to the problems below. All plots must be included in the submitted PDF. Submit Matlab scripts as .m files and Simulink models as . six files. For each problem, submit no more than one file of each type, titled Problem_#.m or Problem_#. six as appropriate. Problem 1. Consider the operational amplifier circuit shown in Figure P6.33 on page 185 of Modeling and Analysis of Dynamic Systems, 3rd edition. The amplification of the op-amp is A. First consider the case where A is not large. The input-output differential equation, where the input and output are e, and e, respectively, is given by RIREC ( 1+ *) cot ( RI + R1 + Ry ) Co RA(R, + R2) Ra + RA ei + Ra + RA (1) Assume that the amplification A -> co. Write the resulting input-output differential equa- tion. Next, let C = 2 F and R1 = R2 = Ra = RA = : 0, and express the input-output differential equation in state-space form i = ar + bei, Co = cr + dei, where the state variable is r = 26. - ei. In other words, find the coefficients a, b, c, d. Problem 2. Consider your state-space model from Problem 1. Use Matlab's ode45 function, Matlab's 1sim function, OR Simulink to solve the state-space equations, where r(0) = 0 and e(t) = e-1/4cos 4xt. Please turn in all code and a plot of the output voltage es(t) for 15 s with all axes correctly labeled and with units specified. If you need help using a Matlab function, then type "help [function name]" in Matlab. For example, if you need instructions on how to use the 'Isim' function, then type "help Isim".Carruthers & Co was founded at the end of June 2017. The company has a capital of $40,000 of which f25,000 invested in fixed assets (plants and machinery). The company budgeted data for the first six months (July to December 2017) are as follows in Tables 1 and 2 shown below: Table 1. Budgeted data for six months (July to December 2017) Sales E600,000 Materials used E240,000 Materials purchased during the period E260,000 Wages E180,000 Overheads (including depreciation of {2,000) E140,000 Table 2. Budgeted data for six months (July to December 2017) Expected cash receipts and payments for six months Receipts from sales Payments for materials July 40,000 60,000 August 50,000 60,000 September 50,000 20,000 October 70,000 20,000 November 120,000 20,000 December 150,000 20,000 Total $480,000 E200,000 Overheads and wages are paid evenly each month. Carruthers & Co is convinced that the business will be profitable in its first six months of trading and is planning to use the surplus cash generated from the business as a basis for expanding the operations of the business early next year. Required: a) Produce a simple profit and loss account for the first six months July to December 2017. Can you confirm Carruthers & Co.'s expectations regarding their business prospects? (40 marks) b) Produce a cash budget for the six months identifying the maximumAugust 50,000 60,000 September 50,000 20,000 October 70,000 20,000 November 120,000 20,000 December 150,000 20,000 Total E480,000 (200,000 Overheads and wages are paid evenly each month. Carruthers & Co is convinced that the business will be profitable in its first six months of trading and is planning to use the surplus cash generated from the business as a basis for expanding the operations of the business early next year. Required: a) Produce a simple profit and loss account for the first six months July to December 2017. Can you confirm Carruthers & Co.'s expectations regarding their business prospects? (40 marks) b) Produce a cash budget for the six months identifying the maximum additional funding the owner will need to raise. (40 marks) c) Advise Carruthers & Co on the action they should take to improve the company cash-flow position. (provide your answers in max. 200 words) Five valid reasons - 4 marks per valid reason (20 marks) Total 100 marks