$(10$ points$)$ A company is deciding upon a number of options for manufacturing their latest widget. The cost to the company depends

on the number of widgets they intend to produce and which option they choose. Let $x$ be the number of widgets they intend to

produce. The dollar cost for the first option, c$1,$ is found from:

$c_1=100+0\mathrm{.}1x+0\mathrm{.}01x^2$

The cost for the second option, c$2,$ is found from:

The cost for the third option, c$3,$ is found from:

$c_2=50+0\mathrm{.}5x+0\mathrm{.}02x^2$

$c_3=10+0\mathrm{.}07x+0\mathrm{.}1x^2$

Plot the cost for all three options on the same graph so that you can clearly show graphically the range of widgets which needs to

be produced for each option to be the most economically viable for the company. Then, have your $m-$file determine the numerical

range of widgets for each option to be the most economical, and display your results.