A computer manufacturing company has two assembly plants, plant A and plant B, a

Question

A computer manufacturing company has two assembly plants, plant A and plant B, and two distribution outlets, Outlet 1 and outlet 2. Plant A can assemble at most 750 computers a month, and plant B can assemble at most 750 computers a month. Outlet 1 must have at least 850 computers a month, and outlet 2 must have at least 450 computers a month. Transportation costs for shipping one computer form each plant to each outlet are as follows: $4 from plant A to outlet 1; $5 form plant A to outlet 2;$6 from plant B to outlet 1;$3 from plant B to outlet 2. Find a shipping schedule that will minimize the total cost of shipping the computers form the assembly plants to the distribution outlets. Ship ____ computers from Plant A to outlet I Ship____ computers form Plant A to outlet II Ship ____ computers form Plant B to outlet I Ship ____ computers form Plant B to outlet II The minimum shipping cost is ___.

Explanation / Answer

we have to MINIMIZE the total cost of shipping Name x1 = number of computers assembled in plant A and transported to outlet I x2 = number of computers assembled in plant A and transported to outlet II x3 = number of computers assembled in plant B and transported to outlet I x4 = number of computers assembled in plant B and transported to outlet II Then we have shipping cost = 6 x1 + 5 x2 + 4 x3 + 8 x4, to be minimized we have as constraints x1+x2=1000 I have a simplex program that calculates maximisation problems so i will convert this to a maximising problem : maximise -6x1-5x2-4x3-8x4 under the constraints x1+x2

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