Peaches are to be transported from three orchard regions to two canneries. Inter

Question

Peaches are to be transported from three orchard regions to two canneries. Intermediate stops at a consolidation station are possible.

Orchard

Station

Cannery

Riverside

Waterford

Sanderson

Sunny Slope

Northside

Millville

Old Farm

The available supplies at the orchards, demands at the canneries, and shipping costs are illustrated in the tables below.

Waterford

Northside

Supply

Riverside

$5

$5

1500

Sunny Slope

$4

$3

1500

Old Farm

$6

$2

2000

Sanderson

Millville

Waterford

$2

$4

Northside

$5

$9

Demand

2000

3500

Find the lowest cost transshipment schedule using linear programming.

How many peaches are sent from Riverside to each of the consolidation stations?

How many peaches are sent from Sunny Slope to each of the consolidation stations?

How many peaches are sent from Old Farm to each of the consolidation stations?

How many peaches are sent from Waterford to each of the canneries?

How many peaches are sent from Northside to each of the canneries?

What is the total cost of transshipment?

Which cannery(ies) has/have unsatisfied demand and by how much?

Orchard

Station

Cannery

Riverside

Waterford

Sanderson

Sunny Slope

Northside

Millville

Old Farm

Explanation / Answer

Avaialble supplies are 1500 ( Riverside )+ 1500 ( sunny dlope ) + 2000 ( OLD farm) = 5000

Total Demand = 2000 ( sanderson) + 3500 (milleville ) = 5500

Cheapest transportation cost can be determined as follows

Route :

1) consider cost from Riverside to Sanderson route

we see Reverside to any intermdiate stop is same ie.$5. But Waterford to Sanderson is $2 less than north side to Sanderson. So the best route is

Riverside -> waterford-> Sanderson

Cost = $5 + $2 = $7

Consider Route from :Riverside to Millville

Cost from Riverside to Waterford to Millville = $5 + $4 =$9

Riverside to north side to millville = $5 + $ 9 = $14

So best route is Riverside -> Waterford -> Millville

Cost = $5 +$4 = $9

2) Now Consider route from Sunny slope to Sanderson

if Peaches are sent from Sunny slope to waterford to Sanderson , cost = $4+@2 = $6

cost of Sunnyslope to Nothside to sanderson = $3 + $5 = $8.

So best route from sunnyslope to Sanderson is

Sunnyslope->waterford -> sanderson

Consider route from Sunny slope to Millville

Again cost of Sunny slope to Waterford to Millville is $4 + $4 = $8 which is less than Sunny slope to North side to Millville = $3+$9 = $12

So Best route is Sunny slope -> Waterford -> Millville

3)

Consider rout from Old Farm to Sanderson

OLD farm to Waterford to Sanderson cost is $6 + $ 2 = $8

Old farm to North side to Sanderson cost is $ 2 + $5 = $7

So best route isOld farm to North side to Sanderson

Consider rout from Old Farm to Sanderson

OLD farm to Waterford to Millville cost is $6 + $ 4 = $10

Old farm to North side to Millville cost is $ 2 + $9 = $11

So best route is Old farm to Waterford to Millville.

Question 2: How many peaches are sent from Riverside to each of the consolidation stations?

Riverside will send 750 to Sanderson and 750 to Millville

Question 3 : How many peaches are sent from Sunny Slope to each of the consolidation stations?

Sunny slope will send 750 to Sanderson and 750 to Millville

balance required to Sanderson = 2000- [ 750 ( From riverside ) + 750 ( From sunny slope) ] = 500

Balance required to Millville =3500 -[ 750 ( From riverside ) + 750 ( From sunny slope) ] = 2000

Question 4:

How many peaches are sent from Old Farm to each of the consolidation stations?

Old Farm will send 500 to Sanderson

balance availablity of Old Farm = 2000 - 500 ( sent to Sanderson) = 1500

So only 1500 will be sent from Old farm to Milleville .

Question 5:

How many peaches are sent from Waterford to each of the canneries?

As per above linear programing all the peaches of Riverside and Sunny slope sent through Waterford

Old farn sends peaches to millville via waterford.

So total peaches sent through Waterford = 1500 + 1500 + 1500 = 4500

Question 6:

How many peaches are sent from Northside to each of the canneries?

Only peaches sent from Old farm to Sanderson are sent through North Side i.e 500

Question 7:

What is the total cost of transshipment?

Total cost of transportation = total cost from riverside + total cost from sunny slope + total cost from Old farm

Total Cost from riverside = cost to Sanderson + Cost to Millville

Total Cost from riverside = $ 7 + $ 9 = $16

Total Cost from Sunny slope = cost to Sanderson + Cost to Millville

Total Cost from Sunny slope = $6+ $8 = $14

Total Cost from Old Farm = cost to Sanderson + Cost to Millville

Total Cost from Old Farm = $7 + $ 10 = $17

Total cost of transportation = $16 + $14 + $17 = $47

Question 8:

Which cannery(ies) has/have unsatisfied demand and by how much?

Millville has unsatisfied demand = 3500 (Demand ) - 750 ( Sent from Riverside ) - 750 ( sent from Sunny Slope ) - 1500 ( sent from Old Farm ) = 500

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