4,5, and 6 please 4) Some information from the Solver report is provided in the

Question

4,5, and 6 please

4) Some information from the Solver report is provided in the tables below, XB2-800, shadow prices of location B (Bakersfield) is S3, What is the shadow price at demand center 2 (L.A)? [ie, what is the value of v2 in the table below? 5) Based on information provided in the tables below, what is the value of XBI? 6) What is the Marginal Loss of shipping from location B (Bakersfield) to demand center (SF)? Unit Shipping cost CAI = $3 XA1 = 300 XA2 100 XB1 = ? A2 $12 Shadow Price $3

Explanation / Answer

(4)

Given that XA1 has a positive (non-zero) optimal solution, the first constraint of the dual will be binding i.e. we can write

-yA + 0yB + v1 + 0v2 3 as -yA + 0yB + v1 + 0v2 = 3

or, -yA + v1 = 3 -------------(1)

Given that v1 = 3, from (1), we can say that yA = 0

Again note the second constraint of the dual. it is -

-yA + 0yB + 0v1 + v2 12
or, simply, yA + v2 12
Since yA = 0, v2 12

As this is a binding constraint (as XA2 has a positive optimal value of 100), we will replace the '' with '=' sign and confirm that v2 = 12

(5)

The demand of 1 was 300 which is already fulfilled by A as XA1=300, So, no more flow from B to 1 i.e. XB1=0.

(6)

Note that the cost incurred in flow of one unit from A to 1 is $3 and for B to 1 it is $9. So, there is a marginal loss of $9 - $3 = $6 in selecting location B for demand center 1.

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