let

x = the number of apples

y = the number of peaches

we have the following constrains:

At least 500 peaches and 700 apples must be picked daily to meet minimum demands from her buyers:

y >= 500

x >= 700

The workers can pick no more than 1400 peaches and 1200 apples daily:

y <= 1400

x <= 1200

The combined number of peaches and apples that the packaging department can handle is 2300 a day:

x + y <= 2300

The constrain are:

500 <= y <= 1400

700 <= x <= 1200

x + y <= 2300

The objective function is the profit F(x , y) = 0.25x + 0.20y

we will draw the graph of the system and find the corner points:

click here to see the graph:

the corner points are:

(700, 500), (1200, 500), (700, 1400), (900, 1400), (1200, 1100)

the value of F(x, y) in each of this points is:

F(700, 500) = 0.25*700 + 0.20*500 = $275

F(1200, 500) = 0.25*1200 + 0.20*500 = $310

F(700, 1400) = 0.25*700 + 0.20*1400 = $455

F(900, 1400) = 0.25*900 + 0.20*1400 = $505

F(1200, 1100) = 0.25*1200 + 0.20*1100 = $520

1200 apples and 1100 peaches should be picked up daily for maximum income.

the maximum income is $520.