Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

Graph B

No

Inside

Step-by-step explanation:

Let, the number of apples = x and number of peaches = y.

It is given that the farmer can afford maximum of 54 acres.

Thus, x + y ≤ 54.

Also, apples require 3000 gallons of water and peaches require 800 gallons of water each day.

Since, maximum amount of water is 80,000 gallons per day,

We get, 3000x + 800y ≤ 80,000.

It is required to maximize the profit given by z = 3400x + 1600y.

Thus, the system of equations becomes,

z = 3400x + 1600y

3000x + 800y ≤ 80,000.

x + y ≤ 54.

Plotting these equations gives the following graph.

We can see that the graph obtained is equivalent to Graph B.

Further, we know that the maximum value of the objective function z = 3400x + 800y is obtained at the boundary point of the solution region.

Thus, any point inside the solution region will give a feasible solution not maximum solution.

Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.