◦ 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?
Blue: 500 tons
Blue:
If she grows only POTATO, total quantity of POTATOES produced =
500 tons
If she grows only CORN, total quantity of CORN produced =
500 tons
Red:
If she grows only POTATO, total quantity of POTATOES produced =
900 tons
If she grows only CORN, total quantity of CORN produced = _______________________
◦ How many tons of corn could Farmer Blue produce on a single acre?
_________________
◦ How many tons of potatoes could Farmer Blue produce if she only grew potatoes?
_______________________
◦ How many tons of corn could Farmer Red produce in total? How many tons of potatoes?
________________________
◦ For every ton of potatoes that Farmer Blue grows, how many tons of corn can she grow?
____________________
◦ To calculate the potato: corn tradeoff, does it matter whether you use the per-acre or total farm yields?
____________________
◦ Is each farmer equally good at growing one crop as the other?
____________________
◦ What mathematical concepts you are using to do the above tasks?
____________________
If we write corn in terms of potatoes, the equations for BLUE Farmer would be P = 500 – C.
Equation for RED Farmer, P = 900 – 3C
Complete the following table if both farmers grow crops in different combination:
For Blue Farmer
➢If 300 Tons of potatoes are yield then how many tons of corn will be yield?
__________________
➢If 100 tons of corn is yield then how many tons of potatoes will be yield?
__________________
◦ For Red Farmer
➢If zero tons of corn is yield then, how many tons of potatoes will be yield ?
_______________
◦ Imagine the two farmers make a deal:
➢Farmer Blue will grow only corn and Farmer Red will grow only potatoes.
➢Then they’ll trade: two tons of potatoes for one ton of corn. ➢i.e. P = 2C
◦ Plot how much of each crop Farmers Blue and Red could have after trading.
Trading relation between Potatoes and Corn is : They’ll trade: two tons of potatoes for one ton of corn.
How do you think Farmers Blue and Red should decide who grows corn and who grows potatoes?
_______________________________________________________________________________
What kind of mathematical analysis helped you decide the above trade off?
______________________________________________________________________________
Can you suggest any other trade off pattern which can lead to better profits for both farmers?
_______________________________________________________________________________
Answers
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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Question:
◦ For every ton of potatoes that Farmer Blue grows, how many tons of corn can he grow?
◦ To calculate the potato: corn trade-off, does it matter whether you use the per-acre or total farm yields?
◦ Is each farmer equally good at growing one crop as the other?
◦ What mathematical concepts you are using to do the above tasks
Answer:
(i) Farmer Blue can grow 1 ton of corn per acre for every ton of potatoes he grows. Therefore, for every ton of potatoes, he can also grow 1 ton of corn.
(ii) The potato: corn trade-off does not depend on whether we use the per-acre or total farm yields. In both cases, the ratio of the yields remains the same. However, if we want to compare the total yields of potatoes and corn for each farmer, we need to use the total farm yields.
(iii) No, Farmer Blue is better at growing both crops than Farmer Red. Farmer Blue can grow 5 tons of corn or potatoes per acre, while Farmer Red can only grow 2 tons of corn or 6 tons of potatoes per acre.
(iv) The mathematical concepts used to solve the above tasks are ratios, proportions, and basic arithmetic operations (multiplication, division, addition, subtraction).
Hope you find it helpful!