Argo produts makes two tpes of fertilizers that are sold in

Argo produts makes two tpes of fertilizers that are sold in 50 lb bags. a 50 lb bag of fertiliser A has 5 lb of nitrogen, 10 lb of phosphorus, and 20 lb of Potassium. Fertilizer B contains 6 lb of nitrogen, 4 lb of phosphorus, and 4 lb of potassium. Argo products has 1800 lb of nitrogen, 1600 lb of phosphorus and 2600 lb of potassium on hand.

a) write a sustem of linear inequalities that gives the restrictions to be placed on the number of bags of each type of firtizer that Argo Products can manufacture.

b) Graph the solution set S for the system of linear inequalities found in part (a).

c) Is it possible for Arogo Products to make 100 50 lb bags of Fertilizer A and 200 50 lb bags of Fertilizer B?

Solution

Restrictions are:

5A+6B<=1800

10A+4b<=1600

20A+4B<=2600

Solving II and III we have A<=100 and B<=150

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Take i and III

B<=230 and A<=84

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I and II together gives

A<=60 and B<=250

Taking into account all the possibilities

c) For 100 A and 200 B bags

Hence solution is below (60,250) and (100,150)

c)(100,200) is not below this limit

Hence not possible.