1.) A catering company makes three kinds of jello salad-orange, strawberry, and

Question

1.) A catering company makes three kinds of jello salad-orange, strawberry, and lemon. It supplies two outlet stores, Outlet A and Outlet B. The company can make up to 14 trays of orange, 20 trays of strawberry, and 24 trays of lemon per day. Outlet A needs at least 20 trays of jello per day and Outlet B needs a least 10 trays of jello per day. The transportation costs for shipping trays from the company to the outlests are given below: $4 for Outlet A and $1 for Outlet B, Strawberry is $1 for Outlet A and $4 for Outlet B, and Lemon is $5 for Outlet A and $5 for Outlet B.

Shipping Charges

Type Of Jello

Outlet A

Outlet B

Orange

$4

$1

Strawberry

$1

$4

Lemon

$5

$5

Formulate a linear programming problem that will determine a shipping schedule that will minimize the cost of transporting the jello salads to fill the needs of the two outlets. DO NOT SOLVE.
Let x1= number of trays of orange shipped to Outlet A
x2= number of trays of strawberry shipped to Outlet A
x3=number of trays of lemon shipped to Outlet A
x4=number of trays of orange shipped to Outlet B
x5=number of trays of strawberry shipped to Outlet B
x6=number of trays of lemon shipped to Outlet B

Type Of Jello

Outlet A

Outlet B

Orange

$4

$1

Strawberry

$1

$4

Lemon

$5

$5

Explanation / Answer

Transportation costs for Outlet A can be given as 4x1+x2+5x3

Transportation costs for Outlet B can be given as x4+4x5+5x6

Total cost of Transportation is (4x1+x2+5x3+x4+4x5+5x6) which is to be minimized.

The Constraints can be given as

From Company Production : x1+x4<=14;x2+x5<=20;x3+x6<=24

Outlet A Requirements : x1+x2+x3>=20

Outlet B Requirements : x4+x5+x6>=10

and x1>=0 ; x2>=0 ; x3>=0 ; x4>=0 ; x5>=0 ;x6>=0 Non Negative Deliveries

Hence the NLPP Can be written as

Minimize (4x1+x2+5x3+x4+4x5+5x6) subject to the constraints x1+x4<=14 ; x2+x5<=20 ; x3+x6<=24 ; x1+x2+x3>=20 ; x4+x5+x6>=10 ; x1>=0 ; x2>=0 ; x3>=0 ; x4>=0 ; x5>=0 ;x6>=0

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