Compute the minimum cost of oil and the optimum tanker size

Reference no: EM132164209

Assignment - Please put all your computer scripts and results including tables and figures into a word/pdf file.

1. The cost of refined oil when shipped via the Malacca Straits to Japan in dollars per kiloliter was given (Uchiyama, 1968) as the linear sum of the crude oil cost, the insurance, customs, freight cost for the oil, loading and unloading cost, sea berth cost, sub-marine pipe cost, storage cost, tank area cost, refining cost, and freight cost of products as

c = c_c + c_i + c_x + (2.09x10⁴t^-0.3017)/360 + (1.064x10⁶at^0.4925)/52.47q(360) + (4.242x10⁴at^0.7952+1.813ip(nt+1.2q)^0.861)/52.47q(360) + 4.25x10³a(nt+1.2q)/52.47q(360) + (5.042 x 10³q^-0.1899)/360 + 0.1049q^0.671/360

where -

a = annual fixed charges, fraction (0.20)

c_c = crude oil price, $/kL (12.50)

c_i = insurance cost, $/kL (0.50)

c_x = customs cost, $/kL (0.90)

i = interest rate (0.10)

n = number of ports (2)

p = land price, $/m² (7000)

q = refinery capacity, bbl/day

t = tanker size, kL

Given the values indicated in the parentheses, use a computer code to compute the minimum cost of oil and the optimum tanker size t and refinery size q by Newton's method. (Note that 1 kL = 6.29bbl)

2. A culture of bacteria increases at a rate that is proportional to the number of bacteria present at that instant. Assuming that the number doubles every 5 hours, a biomedical engineer can estimate the number of bacteria present at a future time using the differential equation

dy/dt = ky

where y is the number of bacteria present at time t.

(a) Determine the value of k.

(b) Assuming at time t = 0,y = 1, use the adaptive second order Runge-Kutta to calculate and plot the number of bacteria present y as a function of time t from 0 to 12 hours.

3. Enzymatic reactions are used extensively to characterize biologically mediated reactions in environmental engineering. Proposed rate expressions for an enzymatic reaction are given below where [S] is the substrate concentration and v₀ is the initial rate of reaction. Which formula best fits the experimental data? (Here k and K are fining parameters.)

v₀ = k[S], v₀ = k[S]/(K+[S]), v₀ = k[S]²/(K+[S]²), v₀ = k[S]³/(k+[S]³)

[S], M	Initial Rate, 10^-6 M/s
0.01	6.3636 x 10^-5
0.05	7.9520 x 10^-3
0.1	6.3472 x 10^-2
0.5	6.0049
1	17.690
5	24.425
10	24.491
50	24.500
100	24.500

Reference no: EM132164209

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