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A Sa D S Ds Ds

In: Business and Management

Submitted By alihhmb
Words 251
Pages 2
Alabama Atlantic would like to determine the optimal shipping routes for its lumber and the amount to be shipped on each route, in order to minimize the total equivalent uniform annual cost. It is my understanding that the company has three sources of wood, with annual availabilities of 15, 20, and 15 million board feet respectively. Additionally, the company has 5 markets it sells to, which have annual demands of 11, 12, 9, 10, and 8 million board feet respectively. Because the estimated supply and demand of wood is in equilibrium, it is important to meet the full demand in each market. It is also important that total amount shipped does not exceed the available supply.

Alabama Atlantic has two possible methods to ship the wood. They can either ship it by train or by ship. Depending on the specific source and market, it can be less costly to use one method over the other. However, it is important to note that using ships may require a large capital investment.

I have had a chance to determine the potential shipping plans for Alabama Atlantic and have analyzed the company’s situation. I was able to solve this as a linear programming problem using Microsoft Excel, however some assumptions had to be made. First, the production costs are assumed to be the same at each source, so that the only relevant costs are for shipping. Second, the cost of shipping is assumed to be constant no matter what quantity is shipped.

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Laplace Transform and Its Application

...= f (t), y(t) = f (t). In differential equation applications, y(t) is the sought-after unknown while f (t) is an explicit expression taken from integral tables. Below, we illustrate Laplace’s method by solving the initial value problem y = −1, y(0) = 0. The method obtains a relation L(y(t)) = L(−t), whence Lerch’s cancellation law implies the solution is y(t) = −t. The Laplace method is advertised as a table lookup method, in which the solution y(t) to a differential equation is found by looking up the answer in a special integral table. 7.1 Introduction to the Laplace Method 247 Laplace Integral. The integral is called the Laplace N integral of the function g(t). It is defined by limN →∞ 0 g(t)e−st dt and depends on variable s. The ideas will be illustrated for g(t) = 1, g(t) = t and g(t) = t2 , producing the integral formulas in Table 1. ∞ −st dt...

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