Acme Mfg., Inc. makes three kinds of lawn tractor in one of its many plants, the

Question

Acme Mfg., Inc. makes three kinds of lawn tractor in one of its many plants, the Mitymite, the All-purpose and the Powerhouse. In terms of labor used, the Mitymite requires 3 hours for parts acquisition, 2 hours for assembly and 1 hour for packaging and shipping. The All-purpose requires 4 hours for parts acquisition, 3 hours for assembly and 2 hours for packaging and shipping. Finally, the Powerhouse requires 4 hours for parts acquisition, 6 hours for assembly and 2 hours for packaging and shipping. If Acme has available a total of 480 hours of labor for parts acquisition, 400 hours for assembly and 200 hours for packaging and shippping and management wants all of the hours in each category of labor utilized in that category in the production of these very popular tractors, how many Mitymites should be produced so no unused time is left over?

Explanation / Answer

note:first this problem has to be seen as a linear equation.there are three variables.that is the number of tractors produced.

let the number of tractors Mitymite produced is :x.

let the number of tractors of all-purpose produced is: y

no.of powerhouse is:z.

now mitymite takes 3 hours,all-purp takes 4hours,power takes 4 hours for acquisition

that means 3x+4y+4z=480. only this condition will satisy the ful utilisation of all hours of acquisition.

in the same way 2x+3y+6z=400. for assembly

1x+2y+2z=200. for packaging.

therefore the 3 equations are

3x+4y+4z=480 - 1st equation

2x+3y+6z=400 -2nd equation

1x+2y+2z=200 -3rd equation

now the simlification is just simple by using matrix methods are just by solving the equations.

x=80. y=40 ,z=20

therefore the no.of mitymites to be produced is =80

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