a$.$ Formulate and solve an LP model to maximize the profit

contribution from the two vitamin C products. How many

kilograms of vitamin $C$ capsules and tablets should the

company produce each week? What is the maximum

profit the company can make?Many vitamin $C$ products are made from ascorbic acid,

which can be derived from corn. A small dietary supple$-$

ment company makes two types of vitamin $C$ supplements:

capsules and chewable tablets. To produce $1$ kilogram

of vitamin C capsules, $30$ kilograms of corn, $2\mathrm{.}3$ hours of

manufacturing time, and $2$ hours of packaging time are

required. To produce $1$ kilogram of vitamin $C$ tablets,

$40$ kilograms of corn, $4\mathrm{.}2$ hours of manufacturing time,

and $1$ hour of packaging time are required. Each week,

the company receives $2,000$ kilograms of corn from its

suppliers and allocates $180$ hours of equipment time for

manufacturing and $110$ hours of packaging equipment

time for vitamin C supplements. One kilogram of vitamin C

capsules generates a profit of $$9\mathrm{.}50,$ and one kilogram of

chewable tablets generates a profit of $$12.$