Question

1. A large oil company has hired you as part of their engineering team that is planning all of

the details for a new drill site. The crude oil will be stored in large cylindrical tanks. The

following restrictions apply to the tanks you can purchase:

(a) Tank heights must be in full meters

i. The maximum tank height for sale is 12 meters

ii. The minimum tank height for sale is 7 meters

(b) All tanks have a diameter of 4 meters

(c) Each tank must be able to be drained in 2 hours or less

(d) The flow rate cannot exceed 0.0175 m3/s

(e) *you will need to compute the maximum height of a tank that can be drained in 2 hours

with the max flow rate to determine which tanks you can buy

Other problem data and restrictions

(a) The cost of each tank is $5000*h where h is the height of the tank in meters

(b) Your objective is to minimize the cost of the tanks needed to store the oil

(c) You need to be able to store 500 cubic meters of crude oil at a time

i. o *you will need to compute the volume of oil that can be stored in each size tank

(d) You can have at most 7 tanks

(e) You cannot buy a fraction of a tank

(f) You will pay a fixed shipping cost of $2000 for each different tank size you purchase

i. ex: if you buy 1 tank with height 7m and 1 tank with height 8m, you will pay $4000

total in shipping

ii. ex: if you buy 3 tanks with height 6m, you will pay a total of $2000 in shipping

Formulate an IP to decide how many of each size tank to buy so that the company can store

all of the crude oil they need at a minimum cost. It is recommended that you handle your

tank computations in excel before writing the IP.

Reference & Reminders

The volumetric flow rate Q is the volume of fluid that is passing through a given cross sectional area per unit time. It is important to know the flow rate because it can be used to determine how deep a well should be dug or appraised to reach a reservoir.

Q = (Volume)/(Time)

unit example : meters³/second

Answer 1