Phase $2$

Food Manufacturing Industry: A Case Study

A manufacturing company produces three types of food: Type $1,$ Type $2,$ and Type $3.$ The profit from selling

each kilogram of Type $1,$ Type $2,$ and Type $3$ is $$1,$ $$2,$ and $$3$ respectively. The production of these food types

requires two types of raw materials: A and B and manpower

Each kilogram of Type $1$ requires $1$ kg of A$,$ and $3$ kg of B$,1$ hour of manpower.

Each kilogram of Type $2$ requires $2$ kg of A $,$ and $2$ kg of B$,1$ hour of manpower.

Each kilogram of Type $3$ requires $3$ kg of A $,$ and $1$ kg of B$,1$ hour of manpower.

The company must use at least $6$ kg of A and $6$ kg of B $.$ Additionally, the company has at most $10$ hours of

manpower available.

Question $4$

Formulate an LPP using the above details to maximize the total profit

Question $5$

Using the M method, solve the LPP formulated in Question $4$ and find all the optimal solutions $($if they exist$).$