Question

You have been hired as a consultant to advise Sandbaggers, Inc., a company that purchases silica sand, cleans it, and then sells the silicon dioxide to manufacturers of computer chips. Sandbaggers, Inc., operates two cleaning plants: Plant A and Plant B.

They obtain their supply of silica sand from three independent suppliers (Sand Solutions, Dirt Dudes, and Terra Firma) who are willing to supply the sand in the following amounts and at the following prices:

Supplier	# of Tons	Cost per Ton
Sand Solutions	200	$10
Dirt Dudes	300	$9
Terra Firma	400	$8

Shipping costs in dollars per ton from each supplier to each of the plants are as follows:

	Shipping Cost per Ton
From	To Plant A	To Plant B
Sand Solutions	$1	$1.50
Dirt Dudes	$2	$2.50
Terra Firma	$5	$3

Labor costs at each of the plants are as follows:

	Plant A	Plant B
Labor Cost	$25/ton	$20/ton

Plant capacities are as follows:

	Plant A	Plant B
Maximum Capacity	450 tons	550 tons

The cleaned and processed silicon dioxide is sold at $50 per ton to the chip manufacturers. Sandbaggers, Inc., can sell all they can produce.

Determine how Sandbaggers, Inc. should plan its operation at the two plants to maximize its profit. The executives of Sandbaggers, Inc. would also like to know whether or not both plants are able to operate at maximum capacity and whether they should look for additional suppliers based on your analysis. Prepare a report for the Sandbaggers, Inc. executives detailing your plan and addressing their questions regarding plant capacity and suppliers.

1-An explanation of how you set up the problem and arrived at your answers. This should include:

• A list of your decision variables and what they represent
• Your objective function, what it represents, all math used to obtain it, and a brief explanation of your math
• All constraints, what they represent, and a brief explanation of how you determined the constraints

2-CAN I HAVE THE SOLUTION DONE WITH SIMPLEX METHOD ???

Answer 1

IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE TTHERE TO HELP YOU..ALL THE BEST..

AS FOR GIVEN DATA..

ANSWER:

Decision variable

• How many tons to buy from each supplier
• how many tons to ship from, each supplier to the two plants

Objective

• To maximize total profits(REVENUE- PURCHASE COST-SHIPPING COST-LABOUR COST)

Constraints

• Supplier capacity
• Plant capacity

linear model

Let X1,X2,X3, be the number of tons from the three suppliers to plant 1

Let Y1,Y2,Y3 be the number of tons from the three suppliers to plant 2

Decision variable

X1,X2,X3, Y1,Y2,Y3

Objective

maximize

Z= 50* ( X1+X2+X3+Y1+Y2+Y3) – [10(X1+Y1)+9(X2+Y2)+8(X3+Y3)] – ( 1X1+2X2+5X3 + 1.5Y1+ 2.5Y2+3Y3) – [25(X1+X2+X3)+20(Y1+Y2+Y3)]

Constraints

• (X1+Y1)≤200
• (X2+Y2)≤300
• (X3+Y3)≤400
• X1+X2+X3 ≤ 450
• Y1+Y2+Y3 ≤ 450
• X1,X2,X3,Y1,Y2,Y3 ≥ 0

solution

X1=200 ,X2 =150 ,X3=0

,Y1 =0,Y2-150,Y3-400

Optimal profit - $ 15,275

From sensitivity analysis

The plant A is not operating at maximum capacity. It is utilizing only 350 tons when its capacity is 450 tons ( sensitivity analysis cells d16 & f16)

Looking and at shadow prices and allowable increases of supplier rows in sensitivity analysis,

All the supplier rows show shadow prices 14,14,14.5 with allowable increases. this shows that increasing supplier capacity can help us to increase profit.When the supplier capacity is increased at each supplier there will be an increase in profit by 14, 14 and 14.5 $ respectively, for every ton capacity increased at each unit.

In general, the supplier capacity can be increased by 100 tons at any of these locations as shown in sensitivity analysis cells d18,d19,d20

I HOPE YOU UNDERSTAND..

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THANK YOU...!!