Question

A candy company has 96 kg of? chocolate-covered nuts and 66 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. Complete parts a. and b.

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

Answer 1

Ans:

In Mix A, there is an equal amount of nuts and raisins.
Let x = kg of nuts = kg of raisins.

In Mix B, there is 3 times as much nuts as raisins.
Let y = kg of raisins, then 3y = kg of nuts.

The revenue from Mix A is:

The revnue from Mix B is:

Hence, the total revenue is:

Graph th region:

Point	X coordinate (X1)	Y coordinate (X2)	Value of the objetive function (Z)
O	0	0	0
A	0	32	1216
B	96	0	1344
C	51	15	1284
D	0	66	2508
E	66	0	924

Optimal point,which maximize th revenue is C(51,15)

So,

x=51,y=15

Maximum revenue,z=14*51+38*15=1284