Answer:
1. 7x + 9.5y
2. 1980
Step-by-step explanation:
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.
We have this information:
Nuts Raisins Price
mix A x + x = $ 7.00
mix B 3y + y = $ 9.50
Total: 150 90
Hence, the number of kilograms of each mix should company prepare for the maximum revenue is = 7x + 9.5y
We have these inequalties:
{x≥0y≥0x+3y≤150x+y≤90} (equation 1)
There will be
x+x=2x kg of Mix A at $7.00 per kg.
The revenue from Mix A is:
7(2x)=14x dollars.
There will be
3y+y=4y kg of Mix B at $9.50 per kg.
The revnue from Mix B is:
9.5(4y)=38y dollars.
Hence, the total revenue is:
R=14x+38y (equation 2).
Graph the region determined by [1] and locate its vertices.
You should get:
(0,0),(90,0),(0,50),(60,30)
Test the vertices into [2] and see which vertex produces maximum revenue
(0,0): R=14(0)+38(0)=0 Minimum revenue
(90,0):R=14(90)+38(0)=1260
(0,50): R=14(0)+38(50)=1900
(60,30):R=14(60)+38(30)=1980 Maximum revenue.
