At any moment t = [0;20] a firm and conditions in which it acts are described as in Exercise E11, except additional constraint in a form of a production factor resource:

Exercise E11

A production process in some firm acting in the perfect competition is described by a one-variable production function of a form:

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b(t) = 0.01t + 1. Using the dynamic approach: 1. Solve the profit maximization problem with regard to an input of a production factor and determine time intervals in which the constraint on the production factor resource is binding. 2. Present a trajectory of the demand for a production factor and a trajectory of the firm's maximum profit. 3. Solve the production cost minimization problem assuming that the fixed output level y(t) that the firm wants to achieve in subsequent periods is given by a formula: y(t) = 0.0035 (t +15) + 1.25. Determine time intervals in which the constraint on the production factor resource is binding 4. Present a trajectory of the conditional demand for a production factor and a trajectory of the production minimum cost.