Find the best solutions to your problems with the help of IDNLearn.com's expert users. Join our Q&A platform to get accurate and thorough answers to all your pressing questions.
Sagot :
72 units of wheat must be planted by to farmer for maximum yield and In order to get maximum profit the farmer should plant, 61 units of wheat on land.
Give a brief account on derivative.
In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.
The derivative has a wide range of real-world applications. A function's derivative can be used to find the maxima and minima of the function. Maximizing production, earnings, and minimizing losses are helpful in real life.
To solve the question :
Given:
Planted units of wheat = x
Yield of the farmland Y = [tex]12x- \frac{x^{2} }{12}[/tex]
Cost of production = $110/unit
Revenue from harvest = $60/unit
(a) For maximum yield,
[tex]\frac{dY}{dx} = 0[/tex]
[tex]0= 12x- \frac{x^{2} }{12}[/tex]
[tex]x=72[/tex]
Thus, 72 units of wheat must be planted by to farmer for maximum yield.
(b) Profit (P) = Revenue - Production cost
[tex](60( 12x- \frac{x^{2} }{12})) -(110x)[/tex]
[tex]P=610 x-5x2[/tex]
[tex]\frac{dP}{dx} = 0[/tex]
[tex]610-10x=0[/tex]
[tex]x[/tex] = 61 units
In order to get maximum profit the farmer should plant, [tex]x[/tex] = 61 units of wheat on land.
To know more about, derivative, visit :
https://brainly.com/question/2159625
#SPJ4
The complete question is mentioned below :
Solve the problems below that pertain to a farmer planting wheat.
a. If a farmer plants x units of wheat in his field,
0≤ [tex]x[/tex] ≤ 144, the yield will be [tex]12x- \frac{x^{2} }{12}[/tex] units. How much wheat should he plant for the maximum yield?
_____ units of wheat
b. In the problem above, it costs the farmer $110 for each unit of wheat he plants, and he is able to sell each unit he harvests for $60. How much should he plant to maximize his profit?
_____ units of wheat
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.
