Answer:
25 days
Step-by-step explanation:
Assuming that the farmer waits for n days to get get the maximum profit.
Given that the total number of cows the farmer has, = 100
Currect weight of one cow = 125 kg.
Weight gain rate for one cow = 3 kg/day
So, weight gained by one cow in n days = 3n kg
Therefore, the weight of one cow after n days
Cost for keeping one cow = $5/day.
Cost for keeping one cow for n days = $ 5n
So, Cost for keeping 100 cows for n days
Current market price = 25 pesos / kg = 125 cents / kg [ as 1 peso = 5 cents]
The falling rate of market price = 1 cent /day.
Fall in price in n days cents.
So, market price after n days
By using equations (i) and (iii),
The selling price of one cow after n days cents.
So, the selling price of 100 cows after n days cents.
As 1 $ = 100 cents. so
The selling price of 100 cows after n days .
Now, from equations (ii) and (iv)
Net profit,
To get the maximum profit, differentiate the profit function in equation (v) with respect to n and equate it to zero to get the value of n, i.e
Hence, the farmer has to wait for 25 days to get the maximum profit.