Hi, This is a formulation of linear programming problem. Please sove it without

Question

Hi,

This is a formulation of linear programming problem. Please sove it without softwares.

2. A canning company operates two canning plants. The growers are willing to supply fresh fruits in the following amounts: S1: 200 tons at $11/ton S2: 310 tons at $10/ton S3: 420 ton at $9/ton $42 Shipping costs in $ per ton are: Plant B 3.5 2.5 4 To: Plant A From: Sl S2 2 S36 Plant capacities and labor costs are: Plant A Plant B Capacity 460 tons 560 tons Labor cost $26/ton $21/ton The canned fruits are sold at $50/ton to the distributors. The company can sell at this price all they can produce. The objective is to find the best mixture of the quantities supplied by the three growers to the two plants so that the company maximizes its profits. Formulate the problem as a linear program and explain it .What assumptions have you made in expressing the problem as a linear program

Explanation / Answer

From the 1st statement, S1<=200,  S2<=310,  S3<=420, S1, S2, S3 >= 0

Plant capacities are given , so from this the constraints can be written as

S1+S2+S3<=460

S1+S2+S3<=560

Objective is to maximize the profits : P = 50 (S1+S2+S3) - ((11S1+10S2+9S3)+(3S1+2S2+6S3) + (3.5S1+2.5S2+4S3) + 26(S1+S2+S3)+ 21 (S1+S2+S3))

50 (S1+S2+S3) , this is from the statement of sale to distributors @ 50$

11S1+10S2+9S3, this is from the statement supply cost by 3 growers to the company

(3S1+2S2+6S3) , this is from shipping costs at Plant A

(3.5S1+2.5S2+4S3) , this is from shipping costs at Plant B

26(S1+S2+S3) , this is from labor costs at plant A

21 (S1+S2+S3), , this is from labor costs at plant B

Solve the euqations

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