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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