A company sells four types of boxes (B1,.,B4), ranging in size from 24 to 33 cubic feet (size is measured as volume). The demand and size of each box is given in the table below. The variable cost (in dollars) of producing each box is equal to the box's volume. A fixed cost of $1,000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size. Formulate and solve a shortest-path problem whose solution will minimize the cost of meeting the demand for boxes. B1 B2 B3 B4 Size 33 30 26 24 Demand 400 300 500 700 Considering that this problem can be formulated as a shortest path model, answer the following questions: • Define nodes, arcs, and arc properties in words. Calculate all arc costs and show your calculations in detail. Draw the network graph showing the relevant parameter values on the network. • Formulate the shortest-path model for this problem.

A company sells four types of boxes (B1,.,B4), ranging in size from 24 to 33 cubic feet (size is measured as volume). The demand and size of each box is given in the table below. The variable cost (in dollars) of producing each box is equal to the box's volume. A fixed cost of $1,000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size. Formulate and solve a shortest-path problem whose solution will minimize the cost of meeting the demand for boxes. B1 B2 B3 B4 Size 33 30 26 24 Demand 400 300 500 700 Considering that this problem can be formulated as a shortest path model, answer the following questions: • Define nodes, arcs, and arc properties in words. Calculate all arc costs and show your calculations in detail. Draw the network graph showing the relevant parameter values on the network. • Formulate the shortest-path model for this problem.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

5.
A company sells four types of boxes (B1,.B4) ranging in size from 24 to 33 cubic feet (size is measured as volume). The
demand and size of each box is given in the table below. The variable cost (in dollars) of producing each box is equal to the
box's volume. A fixed cost of $1,000 is incurred to produce any of a particular box. If the company desires, demand for a
box may be satisfied by a box of larger size. Formulate and solve a shortest-path problem whose solution will minimize the
cost of meeting the demand for boxes.
B1 B2 B3 B4
Size
33
30
26
24
Demand 400 300
500
700
Considering that this problem can be formulated as a shortest path model, answer the following questions:
Define nodes, arcs, and arc properties in words. Calculate all arc costs and show your calculations in
detail. Draw the network graph showing the relevant parameter values on the network.
• Formulate the shortest-path model for this problem.

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