Question

Imagine Farmer Blue has 100 acres of land. On his farm, an acre can yield 5 tons of corn or 5 tons of potatoes.

◦ Farmer Red has 150 acres. On her farm, an acre can yield 2 tons of corn or 6 tons of potatoes.

What is the maximum quantity of each crop that Each farmer could grow?

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Blue:

If she grows only POTATO, total quantity of POTATOES produced = ____________________

If she grows only CORN, total quantity of CORN produced = _____________________

Red:

If she grows only POTATO, total quantity of POTATOES produced = ________________

If she grows only CORN, total quantity of CORN produced = _______________________


◦ How many tons of corn could Farmer Blue produce on a single acre?

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◦ How many tons of potatoes could Farmer Blue produce if she only grew potatoes?

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◦ How many tons of corn could Farmer Red produce in total? How many tons of potatoes?

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◦ For every ton of potatoes that Farmer Blue grows, how many tons of corn can she grow?
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◦ To calculate the potato: corn tradeoff, does it matter whether you use the per-acre or total farm yields?

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◦ Is each farmer equally good at growing one crop as the other?

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◦ What mathematical concepts you are using to do the above tasks?
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Answer 1

Blue can grow 500 ton of total production in all either corn or potatoes

Red can grow 900 tons of potatoes

Answer 2

Given :   Farmer Blue has 100 acres of land. On his farm, an acre can yield 5 tons of corn or 5 tons of potatoes.  

Farmer Red has 150 acres. On her farm, an acre can yield 2 tons of corn or 6 tons of potatoes.  

To Find : What is the maximum quantity of each crop that Each farmer could grow?

Solution :

on Blue

Corn  = 5C          C ≤ 100

Potato = 5(100 - C)  = 500 - 5C

on Red

Potatoes = 6P     P ≤ 150

Corn  =  2(150 - P)  = 300 - 2P

Corn  = 5C  + 300 - 2P  = 5C - 2P  + 300

Corn is maximum when C = 100 and P = 0

= 500 - 0 + 300

= 800

Potatoes = 500 - 5C + 6P   = 6P  - 5C  + 500

Potatoes is maximum when

P = 150 , C = 0

= 900 - 0 + 500

= 1400

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