A small food company employs 3 people who work each 8 hours/day to produce two t

Question

A small food company employs 3 people who work each 8 hours/day to produce two types of flour,
types A and B, respectively bringing a profit of 5$ and 3$ per kilo. The production of a type A kilo of flour
requires 2 hours of work(for one person) while producing a kilo of type B flour requires 3 hours (for one person).
Also, each day the production is limited to 6 kilos for type A flour and 8 kilos for type B flour.The aim of the
company is obviously to maximize the daily profit. Formulate a linear programming model for this problem.

Explanation / Answer

Let the number of flour A be x kg

Let the number of flour B be y kg

Maximize Z = 5x + 3y

Constraints

2x + 3Y <= 24 ( since flour A requires 2 hours of work and B requires 3 hours of work, total working hours 3 * 8 = 24)

x <=6

y<=8

Since the profit for X is maximum, hence it will be good to produce 6 kg of A

2(6) + 3(y) <= 24

3y <= 12

y <=4

Hence to maximize the profit it must produce 6kgs of A and 4 kgs of B

Maximum Profit

Z = 6 * 5 + 4 * 3

=> 42$

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