A candy company has 111kg of chocolate- covered nuts and 69kg of chocolate- cove
ID: 2651378 • Letter: A
Question
A candy company has 111kg of chocolate- covered nuts and 69kg of chocolate- covered raisins to be sold as two different mixs. One mix will contain half nuts and half raisins and will sell for $7 per kg. The other mix contain 3/4 nuts and 1/4 raisins and will sale for $9.50 per kg.
a) How many kilograms of each mix should the company prepare for the maximum revenue? Find Maximum revenue.
The company should prepare__kg of the first mix and __kg of the second mix for a maximum revenue of $__.
b) 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 maximum revenue.
The company should prepare__kg of the first mix and __kg of the second mix for a maximum revenue of $__.
Explanation / Answer
Let’s assume A is the number of first mix ( Half nuts : Half Raisins)
Let’s assume B is the number of second mix (3/ 4 nuts: ¼ Raisins)
0.5 A + 0.75 B ( total number of kilograms of nuts consumed)
0.5 A+ 0.25 B ( total number of kilograms of raisins consumed)
Total Revenue is R (A,B)= 7A + 9.5 B
As total number of Kilograms available of nuts is 111 Kg
Hence, 0.5 A + 0.75 B 111 ---------------------- (1)
Similarly 0.5 A + 0.25 B 69 ------------------------(2)
We will ignore the inequalities here to solve the equation,
Put A = 0 in equation (1) we get B= 148
Put A= 0 in equation (2) we get B= 276
Therefore if B is made alone it will be maximum 148 Kg can be produced
Therefore ( A, B)= (0, 148)
Put B = 0 in equation (1) we get A= 222
Put B= 0 in equation (2) we get A= 138
Therefore if A is made alone it will be maximum 138 Kg can be produced
Therefore (A,B)= ( 138, 0)
By subtracting the equation (2) from (1)
We get B= 84,
By putting this value in any of equation we get A= 96
Hence (A, B)= ( 96, 84 )
Therefore we get following combination for production of mix
Option I
Option II
Option -III
(A,B) – (0, 148)
(A,B) -( 138, 0)
(A,B)- (96, 84)
Revenue ( When A is $ 7 per kg and B is $ 9.5 per kg)
( 7*0 + 9.5 *148)
= $ 1406
( 7*138 + 9.5 *)
= $966
( 7*96 + 9.5*84)
= $ 1470
Revenue ( When A is $ 7 per kg and B is $ 11 per kg)
(7*0+ 11*148)
= $1628
(7*138 + 11*0)
= $966
( 7*96 + 11*84)
= $1596
(a)
A is 96 Kg , B is 84 Kg and revenue is $ 1470
(b)
A is 0 kg, B is 148 Kg, Revenue is $ 1628
Option I
Option II
Option -III
(A,B) – (0, 148)
(A,B) -( 138, 0)
(A,B)- (96, 84)
Revenue ( When A is $ 7 per kg and B is $ 9.5 per kg)
( 7*0 + 9.5 *148)
= $ 1406
( 7*138 + 9.5 *)
= $966
( 7*96 + 9.5*84)
= $ 1470
Revenue ( When A is $ 7 per kg and B is $ 11 per kg)
(7*0+ 11*148)
= $1628
(7*138 + 11*0)
= $966
( 7*96 + 11*84)
= $1596
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