I really need to know the variables (x,y), inequality statements and the optimiz

Question

I really need to know the variables (x,y), inequality statements and the optimization statement for the following,?

Rainbow Paints had 1000 gallonss of yellow paint and 1250 gallons of blue paint. These two colors will be mixed and sold as two different shades of green. One mix contains half yellow and half blue. The second mix will contain one-third yellow and two-thirds blue. Rainbow Paints has enough production space to make 2150 gallons. Marketing analysis has shown that the public will buy at least 250 gallons of the first mix and 150 gallons of the second mix. The profit on the first mix is $7.82 and $6.67 for the second mix. How much of each type should be made to have a maximum profit?? What is the maximum profit Rainbow Paints can make???

Any suggestion??,

Explanation / Answer

1/2 x + 1/3 y= 1000 -equation 1

1/2 x + 2/3y = 1250 - equation 2

x+y= 2150 - equation 3

Profit= 7.82x +6.67Y - 4

(1) - (2)

- 1/3y= -250

y= 750

sub. y=750 into (2)

1/2 x + 2/3 (750) =1250

1/2 x + 500= 1250

1/2 x= 750

x= 1500

Maximum profit = 7.82*1500 + 650*6.67

= $16065.50

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