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A candy company has 114kg of​ chocolate-covered nuts and 72kg of​ chocolate-covered raisins to be sold as two different mixes. One mix will contain half nuts and half raisins and will sell for​ $7 per kg. The other mix will contain three fourths nuts and one fourth raisins and will sell for​ $9.50 per kg.The company should prepare how many kg of the first mix and how many kg of the second mix for a maximum revenue of ​how much. The company raises the price of the second mix to​ $11 per kg. Now how many kilograms of each mix should the company prepare for the maximum​ revenue? Find the maximum revenue.

Respuesta :

Answer:

102 kg of mix 1 and 84 kg of mix 2

Explanation:

ITEMS  MIX 1  MIX 2  AVAILABLE

NUTS    0.5     0.75     114

RAISINS 0.5    0.25     72

Let x be the number of kilograms of Mix 1

Let y be the number of kilograms of Mix 2

0.5x + 0.75y < 114......equation 1

0.5x + 0.25y < 72......equation 2

subtracting equation 2 from 1

0.5y = 42

y = 84

substituting 84 for the value of y in equation 1

0.5x + 0.75(84) = 114

0.5x = 114 - 63

0.5x = 51

x = 102

Revenue maximizing function = 7x + 9.5y

substituting the values of x and y into the revenue equation

7(102) + 9.5(84) = $1,512

With the change of price for mix 2, the maximum revenue becomes

7(102) + 11 (84) = $1,638

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