Kate has a 20-square-foot plot of land in her backyard that she uses to grow tomatoes and lettuce. Every square foot of land can produce either 5 tomatoes or 3 heads of lettuce each summer. Her neighbor, Jim, has a 30 - square-foot plot of land that has a lot more shade than Kate's, which is better for lettuce but worse for tomatoes. Every square foot of Jim's land can produce either 3 tomatoes or 6 heads of lettuce.

a) How many tomatoes and heads of lettuce will Kate produce?

b) How many tomatoes and heads of lettuce will Jim produce?

a) Kate will produce 100 tomatoes and 0 heads of lettuce.

b) Jim will produce 0 tomatoes and 180 heads of lettuce.

Explanation:

As climatic conditions are better for tomatoes at Kate's plot of land, she should choose to grow those because of better quality. Also, production of lettuce per square-foot is lower at Kate's land compared to Jim's (3 heads vs 6 heads of lettuce). So on 20-squire-foot Kate could produce 60 heads and Jim - 120 heads of lettuce (2x more). So Kate should avoid production of lettuce due to quality and quantity.

Same explanation can be applied to Jim's production of tomatoes. If Jim produce tomatoes, he will only have quantity of 60 tomatoes at 20-square-foot plot, compare to Kate's 100 tomatoes. So he should avoid production of tomatoes.

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