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Use This Information to Answer the Following Questions The Company Wants to Come Up with an Optimal Shipping

question 35

Essay

Use this information to answer the following questions.
A company can ship its product from any of its three factories,F1,F2,and F3,to any of its retail outlets,R1,R2,and R3.The capacity,demand,and shipping cost information is provided as follows:
$\begin{array}{ll}\text { Demand (units) } & \text { Capacity (units) } \\\text { R1:300 } & \text { F1:250 } \\\text { R2: } 500 & \text { F2: } 350 \\\text { R3:200 } & \text { F3:400 }\end{array}$

$\begin{array}{l}\text { Shipping Cost/unit (\$) }\\\begin{array}{lll}&\mathrm{R} 1 & \mathrm{R} 2& \mathrm{R} 3 \\F1&1&3&2\\F2&3 & 4 & 2 \\F3&2 & 2 & 3\end{array}\end{array}$

The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost.
$Use this information to answer the following questions. A company can ship its product from any of its three factories,F1,F2,and F3,to any of its retail outlets,R1,R2,and R3.The capacity,demand,and shipping cost information is provided as follows: \begin{array}{ll} \text { Demand (units) } & \text { Capacity (units) } \\ \text { R1:300 } & \text { F1:250 } \\ \text { R2: } 500 & \text { F2: } 350 \\ \text { R3:200 } & \text { F3:400 } \end{array} \begin{array}{l} \text { Shipping Cost/unit (\$) }\\ \begin{array}{lll} &\mathrm{R} 1 & \mathrm{R} 2& \mathrm{R} 3 \\ F1&1&3&2\\ F2&3 & 4 & 2 \\ F3&2 & 2 & 3 \end{array} \end{array} The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost. -Use the Sensitivity Report to answer the following questions: a.Suppose that the shipping cost per unit for variable X1 (i.e. ,route F1-R1)increases to $2.00.What impact will this have on the current optimal solution and the objective function value? b.Suppose that the shipping cost per unit for variable X6 (i.e. ,route F2-R3)increases by $2.00 to $5.00.What impact will this have on the current optimal solution and the objective function value? c.Suppose that the factory constraints and the retail outlet constraints become ≤ .What would the optimal solution and the objective function coefficient be? (Hint: The answer to this question is not given in the Sensitivity Report. )$
-Use the Sensitivity Report to answer the following questions:
a.Suppose that the shipping cost per unit for variable X1 (i.e. ,route F1-R1)increases to $2.00.What impact will this have on the current optimal solution and the objective function value?
b.Suppose that the shipping cost per unit for variable X6 (i.e. ,route F2-R3)increases by $2.00 to $5.00.What impact will this have on the current optimal solution and the objective function value?
c.Suppose that the factory constraints and the retail outlet constraints become "≤".What would the optimal solution and the objective function coefficient be? (Hint: The answer to this question is not given in the Sensitivity Report. )

Definitions:

Osmotic Pressure

The pressure required to prevent the flow of a solvent through a semipermeable membrane that separates two solutions with different concentrations.

Solute Concentration

The amount of a substance dissolved in a unit volume of solution.

Selectively Permeable

A property of cellular membranes that allows some substances to pass through while preventing the passage of others.

Osmosis

A process where water molecules move from a region of lower solute concentration to a higher solute concentration through a semipermeable membrane.