The South Hudson Brewery produces beer and ale. Beer sells for $5 per barrel, an

Question

The South Hudson Brewery produces beer and ale. Beer sells for $5 per barrel, and ale sells for $2 per barrel. Producing a barrel of beer requires five pounds of corn and two pounds of hops. Producing a barrel of ale requires two pounds of corn and one pound of hops. One of the proprietors thinks she can get sixty pounds of corn from a farmer near Garrison Station, and the other thinks he can get twenty-five pounds of hops from a vendor near Fishkill. Generally, they sell at least three times as much beer as ale. What should they produce?

Formulate this problem as a Linear Program in standard form. Do not solve.

Give an example from the problem about how the following LP assumptions apply:

Divisibility, Proportionality, Additivity, Certainty, and Feasibility

Explanation / Answer

Let x be the selling units of ale and y beer.

Then prepare table as follows

Our objective is to maxmise Sales

= 5x+2y

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Divisibility applies in the sense how corns and hops are divided among the two products.

Proportion gives the sale of beer to ale.

Additivity is the total corn and hops required

Certainty is the prediction involved in estimating the availability and demand of products

Feasibility is the technique of easily solving.

South Hudson Brewery Available BeerX AleY SP 5 2 Corn(lbs) 5 2 5x+2y 60 Hops(lbs) 2 1 2x+y 25 x>=3y 5x+2y<=60

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