Linear-Programming Applications. Linear-Programming Applications. Constrained Optimization problems occur frequently in economics: maximizing output from a given budget; or minimizing cost of a set of required outputs. Lagrangian multiplier problems required binding constraints.
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Constrained Optimization problems occur frequently in economics:
Lagrangian multiplier problems required binding constraints.
A number of business problems have inequality constraints.
1. constant prices for outputs (as in a perfectly competitive market).
2. constant returns to scale for production processes.
3. Typically, each decision variable also has a non-negativity constraint. For example, the time spent using a machine cannot be negative.
The corner point that maximize the objective function is the Optimal Feasible Solution.
A, B, and C
CONSTRAINT # 1
CONSTRAINT # 1
Maximize p = P1·Q1 + P2·Q2 subject to:
c·Q1 + d·Q2<R1 The budget constraint, for example.
e·Q1 + f·Q2< R2 The machine scheduling time constraint.
where Q1 and Q2 > 0 Nonnegativity constraint.
MinimizeC= R1·w1 + R2·w2 subject to:
c·W1 + e·W2>P1 Profit Contribution of Product 1
d·W1 + f·W2> P2 Profit Contribution of Product 2
where W1 and W2 > 0 Nonnegativity constraint.