3. A pipeline is to transfer crude oil from a tanker docking area to a large oil refinery.

The power required to pump the oil, P in hp, is determined from

P=4x10-¹3-

w²

p'd³

where

w: oil flow rate in lb/hr

p: density of the oil in lb/ft³

d: pipe diameter in ft

The cost incurred, in dollars, is given by

C = 10000d² +170P

where the first term on the right-hand side represents the capital cost of the pipeline and the

second term represents the cost of the pump and its operation. Power in the cost equation can

be calculated using the equation for power above.

a. Create a user-defined function called pumppower with arguments w, rho, and d that

determines the power requirements (P) to pump oil. Use your function in Excel to determine

the power requirements when the oil flow rate is 107 lb/hr, the density is 50 lb/ft³, and pipe

diameter is 2.0 feet [i.e., calculate "=pumppower(1e7,50,2.0)"].

b. Create a user-defined function called cost with arguments d and P that calculates the cost of

a pipeline. Use your answer from part a along with a diameter of 2.0 ft. to calculate the cost

of a corresponding pipeline [i.e., calculate "=cost(2.0,< result from part a >)].

c. Now, use the Solver tool in Excel along with your pumppower and cost functions to adjust

the diameter to determine the minimum cost for a pipeline pumping 107 lb/hr of oil with a

density of 50 lb/ft³. You may want to generate a quick plot of cost as a function of diameter to

verify your solution.