ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.29 : An engineering company that produces small biochemical tools applies Installment Sales Method in its accounting. Let A = Installment Sales, B = Cost of Installment Sales, C = Gross Profit, D = Gross Profit Ratio. In year 20X8, let A = $400, B = $250, C = $150. In year 20X9, let A = $450, B = $315, C = $135. If the value of D = 37.5 % in year 20X8 : (a) find the value of D for year 20X9; (b) calculate the realized gross profit = ED / 100, for year 20X8 when the cash collected from sales is E = $100.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.29 : (a) By trial and error for year 20X8, D = 100 C / A = 100 ($150) / ($400) = 37.5 %. Applying the same formula for year 20X9 will produce D = 100 C / A = 100 ($135) / ($450) = 30 %. (b) Realized gross profit = ED / 100 = $100 (37.5 / 100) = $37.5. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 37 - Calculate the bubble temperature T at P = 85-kPa for a binary liquid with x(1) = 0.4. The liquid solution is ideal. The saturation pressures are Psat(1) = exp [ 14.3 - 2945 / (T + 224) ], Psat(2) = exp [ 14.2 - 2943 / (T + 209) ] where T is in degree Celsius. Please take note that x(1) + x(2) = 1. Please take note that y(1) + y(2) = 1, y(1) = [ x(1) * Psat(1) ] / P, y(2) = [ x(2) * Psat(2) ] / P, * is multiplication. P is in kPa.
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In a Laplace Transform Table, the Laplace transfer function of f(t) is F(s). When d(t) = f(t) then 1 = F(s). When x(t) = f(t) then X(s) = F(s). If d(t) is the impulse of a spring when d(t) = kx(t), then derive the equation for the impulse of a spring as X(s) in term of k. Next question : A controller has a transfer function a and the other controller has a transfer function b. The overall transfer function of both controllers is ab. What is the transfer function overall when both controllers have similar transfer function 1 / (Cs k)?
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PROCESS CONTROL - EXAMPLE 6.3 : The differential equation is 3 dy / dt + 2y = 1 with y(0) = 1. (a) The Laplace transformation, L for given terms are : L (dy / dt) = sY(s) - y(0), L(y) = Y(s), L(1) = 1 / s. Use such transformation to find Y(s). (b) The initial value theorem states that : When t approaches 0 for a function of y(t), it is equal to a function of sY(s) when s approaches infinity. Use the initial value theorem as a check to the answer found in part (a).
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