A candy company has 171 kg of chocolate-covered nuts and 87 kg of chocolate-cove
ID: 3133658 • Letter: A
Question
A candy company has 171 kg of chocolate-covered nuts and 87 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. How many kilograms of each mix should the company prepare for the maximum revenue? Find the maximum revenue. The company should prepare kg of the first mix and kg of the second mix for a maximum revenue of s. The company raises the price of the second mix to S11 per kg. Now how many kilograms of each mix should the company prepare for the maximum revenue? Find the maximum revenue. The company should prepare kg of the first mix and kg of the second mix for a maximum revenue of s.Explanation / Answer
Let us first formulate a linear algorithm
Let 1st Mix be n Kg, and Second Mix be m Kg
Total Amount of Nuts=171=0.5*n+0.75*m-------------------------------------->Condition 1
Total Amount of Raisins=87=0.5*n+0.25*m-------------------------------------->Condition 2
Case-1
Cost of 1st Mix=$7 and Cost of Second Mix=$9.5
Total revenue=7n+9.5m
Hence Maximising Cost subject to n and m under the two conditions gives
n=90Kg, m=169Kg , total revenue=$2226
Case-2
Cost of 1st Mix=$7 and Cost of Second Mix=$11
Total revenue=7n+11m
Hence Maximising Cost subject to n and m under the two conditions gives
n=90, m=168, Total Revenue=2478
Suppose,we were not required to use up all the materials we have,and can leave up some raw materials un used. i.e.,0.5*n+0.75*m<=171 and 0.5*n+0.25*m<=87
Then for the second case->n=0,m=228,Total Revenue=2508
The first case is still the same.
Hence for the second case,take accordingly as to which is required.
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