Q$5$A$-$A local manufacturing plant produces a variety of products. The distribution of the total monthly demand is shown in the table below. Depending on conditions, the average manufacturing cost per item is between $$60$ and $$80($uniform$)$ in integer values and returns from distributors are also uniform, between $120\%$ and $130\%$ of manufacturing costs. There is a fixed cost of $$\frac{2000}{?}$ month for tooling, processing, etc. Build a simulation to estimate the average monthly profit.

$\backslash$table$[[$Demand$,$Probability$],[300,0\mathrm{.}05],[320,0\mathrm{.}10],[340,0\mathrm{.}20],[360,0\mathrm{.}30],[380,0\mathrm{.}25],[400,0\mathrm{.}10]]$

You will get a different value every time you run the simulation. You need to use DATA table to make $1000$ runs, then find $95\%$ confidence interval for the profit expected.

Q$5$B$-$ Generate $500$ samples from a Triangular distribution with parameters $(5,12,20),$ using any method you like BUT do not use a built$-$in Triangular distribution function.

Plot the resulting values to confirm it is Triangular.