Q$1(10$ points$)$: GPA operates a power plant that includes a coal$-$fired boiler to produce steam to drive a generator. The company can purchase different types of coals and blend them to meet the requirements for burning in the boiler. The following table shows the characteristics of the different types of coals:$-$

Type BTU$/$lb $\%$ Ash $\%$ Moisture Cost $($$$/$lb$)$

A $11,50013\%10\%$ $$2\mathrm{.}49$

B $11,80010\%8\%$ $$3\mathrm{.}04$

C $12,20012\%8\%$ $$2\mathrm{.}99$

D $12,10012\%8\%$ $$2\mathrm{.}61$

The required BTU$/$pound must be at least $11,900.$ In addition, the ash content can be at most $12\mathrm{.}2\%$ and the moisture content, at most $9\mathrm{.}4\%.$ Develop and solve a linear optimization model to find the best coal blend for GPA. Explain how the company might reduce its costs by changing the blending restrictions for ash content and moisture content.