Question

In the wake of the Covid-19 pandemic, Honeywell Inc. has orders for 1000 face masks from Richardson and 800 face masks from Plano. Honeywell Inc. has 1200 masks ready in a Frisco facility and 1000 masks in an Irving facility. It costs $10 to ship a mask from Frisco to Richardson, and $7 to ship it from Frisco to Plano. It costs $9 to ship a mask from Irving to Richardson and $12 to ship it from Irving to Plano. How many masks should Honeywell Inc. ship from each facility to Richardson and Plano to fulfill the orders at the minimum cost? (i) (2 points) What are the decision variables?(ii) (3 points) Write out the objective function.

Answer 1

Decision Variables:

Let number of masks,

From Frisco to Richardson = x1

From Frisco to Plano = x2

From Irving to Richardson = x3

From Irving to Plano = x4

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Objective Function:

We have to minimize the total shipping cost.

Cost from Frisco to Richardson = $10

Cost from Frisco to Plano = $7

Cost from Irving to Richardson = $9

Cost from Irving to Plano = $12

So the objective function is:

MINIMIZE 10*x1 + 7*x2 + 9*x3 + 12*x4

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Constraints:

Frisco has a supply of 1200

Irving has a supply of 1000

Total Supplied from Frisco should not exceed the supply available in Frisco. Same is also applicable for Irving.

x1 + x2 <= 1200

x3 + x4 <= 1000

Richardson has a demand of 1000. Plano has a demand of 800. The demand should be satisfied.

x1 + x3 = 1000

x2 + x4 = 800

No deliveries can be in negative quantity.

x1, x2, x3, x4 >= 0

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Putting in Excel:

Solver Parameters:

As this is a transportation problem, we will solve using Simplex LP.

Optimal Solution:

Hence,

From Frisco to Richardson = 0

From Frisco to Plano = 800

From Irving to Richardson = 1000

From Irving to Plano = 0

Total Cost = $14600.

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