profit quesiton

[needshelp]

My question is:

A 135-kg steer gains 3.5kg/day and costs 80cents/day to keep. The market price for beef cattle is $1.65/kg, but the price falls by 1cent/day. When should the steer be sold to maximize profit.

help is greatly appreciated

the answer is susposed to be 52 days but I can't figure out how to get that.

 

[stapel]

today:
weight: 135
cost: 0.00
value: (1.65)(135)
profit: value - cost

tomorrow:
weight: 135 + 3.5
cost: 0.80
value: (1.65 - 0.01)(135 + 3.5)
profit: value - cost

next day:
weight: 135 + 2(3.5)
cost: 2(0.80)
value: (1.65 - 2(0.01))(135 + 2(3.5))
profit: value - cost

the day after that:
weight: 135 + 3(3.5)
cost: 3(0.80)
value: (1.65 - 3(0.01))(135 + 3(3.5))
profit: value - cost

Study the above until you see the pattern, and then use that pattern to find the formula for the weight, cost, value, and profit "x" days after today.

Eliz.

 

[dagr8est]

Let x = number of days steer is kept

Then...
135+3.5x = weight of steer
1.65-0.01x = price per kilogram
0.8x = cost per day

profit = value-cost
profit = (weight of steer)(price per kilogram)-(cost per day)
profit = (135+3.5x)(1.65-0.01x)-0.8x
profit = 222.75-1.35x+5.775x-0.035x^2-0.8x
profit = -0.035x^2+3.625x+222.75

This is a parabola that opens downwards. Therefore the x value of the vertex (highest point) is what you are trying to find. You could waste your time trying to complete the square or you could just punch it into a graphing calculator and use the trace function to find the vertex. You should get around 51.7 days but you cannot sell it until the full day is up so you round it up to 52 days.