Question

An Indiana corn grower has 1000 bushels of corn that are to be divided between markets in Indianapolis and Fort Wayne. These two markets need at least 100 bushels and 300 bushels. Determine the system of inequalities that describes this situation.

Answer 1

Answer: x + y = 1000 This could be x + y ≤ 1000 depending on how you interpret the distribution. (The markets might not need all )

x ≥ 100 We'll say this is Indianapolis needing a minimum of 100 bushels

y ≥ 300 This is Ft.Wayne needing a minimum of 300 bushels

Explanation:

The distribution could be anything within the darkest shaded area in the attached graph.

For example, if Indianapolis takes only 100 bu, Ft.Wayne could get up to 900bu. If Ft. Wayne takes 300bu, Indy could get up to 700bu.

Or they could each take 500, and the farmer has none left, or they could each take their minimum plus 100 (200 + 400) and the farmer has 600bu left

Answer 2

• x + y = 1000
• x ≥ 100
• y ≥ 300

Explanation:

Let x and y represent amounts to be taken to Indianapolis and Ft. Wayne, respectively. Then you have ...

x + y = 1000 . . . . . . 1000 bushels are to be divided between 2 markets

x ≥ 100 . . . . . . . . . . Indianapolis needs at least 100 bushels

y ≥ 300 . . . . . . . . . Fort Wayne needs at least 300 bushels