A firm has identified that total profit P as a function of the number of units of two products manufactured is given by the following function P = 12x1 + 32x2 – 2x12– 8x22– 1000 where x1 = thousands of units of Product 1 and x2 = thousands of units of Product 2. The number of units of each product that can be produced in the next planning period is constrained by the fact that there are only 12,000 pound of an ingredient that is used in the production of both products available. Both products require
A firm has identified that total profit P as a function of the number of units of two products manufactured
is given by the following function
P = 12x1 + 32x2 – 2x12– 8x22– 1000
where x1 = thousands of units of Product 1 and x2 = thousands of units of Product 2. The number of units of
each product that can be produced in the next planning period is constrained by the fact that there are only
12,000 pound of an ingredient that is used in the production of both products available. Both products require
two pounds of the ingredient per unit produced.
i) Formulate a mathematical model that can be used to determine how much of each product should be
manufactured in the next planning period so as to maximise profit.
ii) Find a solution to your mathematical model.
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