Question

A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and $30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs $50. Fertilizer costs $30 for 1 acre of potatoes and $80 for 1 acre of corn. (a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. (Let x and y be the numbers of acres of potatoes and corn, respectively.)

Answer 1

Answer:

90x+ 50 y ≤  $40,000------  A

30x+ 80y ≤ $ 30,000-------  B

x + y ≤ 500 --- C

Step-by-step explanation:

Let x and y be the numbers of acres of potatoes and corn, respectively.

Then according to the given conditions

90x+ 50 y ≤  $40,000------  A

30x+ 80y ≤ $ 30,000-------  B

x + y ≤ 500 --- C

where both x and y equal to or greater than zero and cannot take a value less than zero.

x + y ≤ 500 --- C

gives us an idea that the total arable land is less or equal to  500 acres.

90x+ 50 y ≤  $40,000------  A

tells us that the total cost of planting potatoes and corn is less or equal to $ 40,000

30x+ 80y ≤ $ 30,000-------  B

tells us that the total cost of fertilizers for  potatoes and corn is less or equal to $ 30,000

In each of these x and y cannot have negative values or less than zero.