Question

A farmer grows two crops, onions and potatoes. Both crops require fertilizer and Miracle Grow throughout the season. A single onion requires 2 lbs of fertilizer and 1 lb of Miracle Grow. A single potato requires 1 lb of fertilizer and 2 lbs of Miracle Grow. The supplier has limited quantities to sell you this year: 4,000 lbs of fertilizer and 5,000 lbs of Miracle Grow. You also know that for every onion grown, you will generate $2.25 profit. For every potato, you generate $2.60 profit.
7. How many onions and potatoes should you grow? a. 4,000 onions and 5,000 potatoes b. 5,000 onions and 4,000 potatoes c. 1,000 onions and 2,000 potatoes d. 0 onions and 4,000 potatoes
8. There is a crisis and not enough Miracle Grow! The supplier can now only sell you 4,000 lbs of Miracle Grow. What is your new product mix? a. 1,000 onions and 2,000 potatoes b. 1,334 onions and 1,332 potatoes c. 998 onions and 1,224 potatoes d. 0 onions and 1,500 potatoes

Answer 1

x= onion
y= potatoes

2x + y <= 4000
x + 2y <= 5000

max
Z = 2.25x + 2.60y

7)

c. 1,000 onions and 2,000 potatoes is correct

8)

now

x= onion
y= potatoes

2x + y <= 4000
x + 2y <= 4000

max
Z = 2.25x + 2.60y

The maximum value of the objective function z=6466.67 occurs at the extreme point (1333.33,1333.33).

Hence, the optimal solution to the given LP problem is : x1=1333.33,x2=1333.33 and max z=6466.67.

b. 1,334 onions and 1,332 potatoes   is correct

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