Wild west produces two types of cowboy hats. A type i hat requires twice as much labor time as a type 2. If all the available labor time is dedicated to type 2 alone, the company can produce a total of 400 type 2 hats a day. The respective market limits for the two types are 150 and 200 hats per day. The revenue is $8 per type 1 hat and $5 per type 2 hat. [
Answers
Given : A type 1 hat requires twice as much labor time as a type 2.
If all the available labor time is dedicated to type 2 alone, the company can produce a total of 400 "type 2" hats a day
The respective market limits for the two types are 150 and 200 hats per day
The revenue is $8 per type 1 hat and $5 per type 2 hat
To Find : Condition for maximum profit
Solution:
Type 2 need T hours
Then Type 1 need 2T hours
Available hrs = 400 T = 400T
Let say A is type 1 & B is type 2
=> 2AT + BT ≤ 400T
=> 2A + B ≤ 400
A ≤ 150
B ≤ 200
Points ( 150 , 100) , ( 100 , 200) as ( 0 ,200) and ( 150 , 0 ) can be ignored just by seeing the point.
Revenue = 8A + 5B
( 150 , 100)
8(150) + 5(100) = 1200 + 500 = 1700
( 100 , 200)
8(100) + 5(200) = 800 + 1000 = 1800
Type 1 = 100
Type 2 = 200
Revenue = 1800 $
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