The owner of a large restaurant is considering how to obtain tablecloths for eac

Question

The owner of a large restaurant is considering how to obtain tablecloths for each of the 7 days that the restaurant is open each week. New tablecloths can be bought for $10 each, and after being used one day they can be cleaned at either Bud's 1- or Mac's 2-day service. Thus, for example, tablecloths used on Monday will be ready for use on Wednesday if sent to Bud or on Thursday if sent Bud charges $3 per tablecloth and Mac's slower service costs 1$ per tablecloth For the 7 days Monday through Sunday, the restaurant needs 110, 100, 160, 120 180, 200, and 120 tablecloths, respectively. After each week is over (late Sunda night) all tablecloths are sold for $2 each because they are unsuitable for anotherr week's use. Formulate a linear programming model to determine how to obtain the require supply of tablecloths at minimum cost

Explanation / Answer

let x1,x2,x3,x4,x5,x6,x7 be towels be purchased on Monday,Tuesday,wed….till Sunday Min 8*(x1+x2+x3+x4+x5+x6+x7)+3*sum of Xi*Ci)+1*sum of(xi*Ji) where Ci+Ji=1 Ci represents washing by bud,Ji represent washing by mac a table cloth purchased on ith day can be washed by bud or mac i=1,7 x1+x6+x5=110 x2+x7+x6=100 x3+x1+x7=160 x4+x2+x1=120 x5+x3+x2=180 x6+x4+x3=200 x7+x5+x4=120 xi>0 for i=1,7

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