A company manufactures two products (p1 and p2) on three machines (m1, m2 and m3). Each of the products must be processed on all three machines. One unit of p1 requires 5h (hours) of processing time on m1, 4h of processing time on m2 and 3h processing time on m3. Machining times required by a unit production of p2 are 2h, 3h and 4h respectively. The machine capacities are 270h, 250h, and 200h per pieces respectively. The unit profits for the products are $100 and $60 respectively. Additionally the manufacturer wants to produce at least five p1 for each p2. Suppose that the produced each product is sold. Formulate a Linear Programming (LP) Model to determine the number of p1 and p2 that maximize the overall profit. (Define the decision variables. Write the objective function, and the constraints. Indicate sign restrictions. Do not try to solve the problem.)
A company manufactures two products (p1 and p2) on three machines (m1, m2 and
m3). Each of the products must be processed on all three machines. One unit of p1
requires 5h (hours) of processing time on m1, 4h of processing time on m2 and 3h
processing time on m3. Machining times required by a unit production of p2 are 2h, 3h
and 4h respectively. The machine capacities are 270h, 250h, and 200h per pieces
respectively. The unit profits for the products are $100 and $60 respectively.
Additionally the manufacturer wants to produce at least five p1 for each p2. Suppose that
the produced each product is sold. Formulate a Linear Programming (LP) Model to
determine the number of p1 and p2 that maximize the overall profit. (Define the decision
variables. Write the objective function, and the constraints. Indicate sign restrictions. Do
not try to solve the problem.)
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