A candy company has 114 kg of chocolate-covered nuts and 72 kg 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.

How many kg of the first mix and how many kg of the second mix should the company prepare for a maximum revenue?

If the company raises the price of the second mix to $11 per kg, how many kilograms of each mix should the company prepare for the maximum revenue?

Find the maximum revenue.

Question

College

Answer :

heavenandholiness heavenandholiness · Answer 1 · 2024-06-26T03:30:59-04:00

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