Q$1(40\%)$ Write a Python program that solves the problem. You could make $t$ continuous.

EXERCISE $8\mathrm{.}3$ A small manufacturing company has purchased a new machine to

manufacture its product. The company estimates that the revenues from using this

machine for $t$ years is given by the formula:

Revenue $=4\mathrm{.}0(1\mathrm{.}0-{0\mathrm{.}75}^t),$

where the units are in millions of dollars. For example, if the machine is used for

$t=4\mathrm{.}0$ years, the revenue would be:

Revenue $=4\mathrm{.}0(1\mathrm{.}0-{0\mathrm{.}75}^4)=$$$2\mathrm{.}73$ million.

If the company stops using the machine, they can sell the machine for its salvage

value. The company estimates that if they sell the machine after $t$ years of use, the

machine's salvage value would be

Salvage value $=\frac{1\mathrm{.}0}{1\mathrm{.}0+t^{\text{'}}}$

where again the units are in millions of dollars. For example, if the machine is sold

after $t=4\mathrm{.}0$ years, the salvage value would be:

Salvage value $=\frac{1\mathrm{.}0}{1\mathrm{.}0+4\mathrm{.}0}=$$$0\mathrm{.}20$ million.

What is the optimal time for the company to sell the machine?