Question

A candy company has 123 kg of chocolate-covered nuts and 75 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 3/4 nuts and 1/4 raisins and will sell for $9.50 per kg. complete parts a and b.

a. How many kilograms of each mix should the company prepare for maximum revenue? find the maximum revenue.

b. how many kilograms of each mix should the company prepare for minimum revenue? find the minimum revenue.

Answer 1

Ans.

Total quantity available of each input

Chocolate-covered nuts (N) - 123kg

Chocolate-covered raisins (R) - 75kg

We have two options of sales mix

Option 1: MIX N:R = 1:1

under this mix total quantity we can make is 150kg (75kg+75kg) because input R is available at max 75kg

total revenue that can be generated under this mix is 150kg X $7 = $1050

Option 2: MIX N:R = 3:1

under this mix total quantity we can make is 164kg (123kg+41kg) because input N is available at max 123kg

total revenue that can be generated under this mix is 164kg X $9.5 = $1558

In light of above calculations

• a. How many kilograms of each mix should the company prepare for maximum revenue? find the maximum revenue.

for maximum revenue i.e, $1558

company should prepare 123kg of Chocolate-covered nuts, 41kg of Chocolate-covered raisins

• b. how many kilograms of each mix should the company prepare for minimum revenue? find the minimum revenue.

for minimum revenue i.e, $1050

company should prepare 75kg of Chocolate-covered nuts, 75kg of Chocolate-covered raisins