Profit = Income minus Expenses

Income = (Total weight of steer, in kg) times (unit price, in $/kg)

Let x = number of days from now when the steer is sold -------------------***

The total weight after x days = (135 +3.5*x) kg

The unit price per kg, after x days = $1.65 -$0.01*x = (1.65 -0.01x) dollars

The expenses after x days = $0.80*x = 0.80x dollars

So,

Profit = Income minus expenses

P = (135 +3.5x)(1.65 -0.01x) -0.80x

P = (135*1.65 -135*0.01x +3.5x*1.65 -3.5x*0.01x) -0.80x

P = 222.75 -1.35x +5.775x -0.035x^2 -0.80x

P = 222.75 +3.625x -0.035x^2 ---------------(i)

Now here, we can solve for maximum P by

a) using the properties of a parabola (because Eq.(i) is a vertical parabola that opens downward and so its vertex is its highest point which gives the maximum P.)

or,b) using Calculus. P is maximum or minimum when dP/dx = 0.

Let me assume you know Calculus, so,

Differentiate both sides of (i) with respect to x,

dP/dx = 3.625 -(0.035)[2x]

dP/dx = 3.625 -0.070x

Set that to zero,

0 = 3.3625 -0.07x

0.07x = 3.625

x = 3.625/0.07

x = 51.7875

or, x = 52 days ---------answer.