# math problem

## Project Description:

a record company needs to produce 100 gold records at one or more of its
three studios. the cost of producing x records at studio 1 is 10 x; the cost of producing y
records at studio 2 is 2y^2; the cost of producing z records in studio 3 is z^2 + 8z
1a. formulate the nonlinear program of producing the 100 records at a minimum cost.
1b. what is the lagrangian associated with your formulation in 1a.?
1c. solve the lagrangian. what is the optimal production plan?
1d. what is the marginal cost of producing one extra gold record?
1e. union regulations require that exactly 60 hours of work be done at studios 2 and 3
combined. each gold record requires 4 hours at studio 2 and 2 hours at studio 3.
formulate the problem of finding the optimal production plan, give the lagrangian, and
give the set of equations that must be solved to find the optimal production plan. it is not
necessary to actually solve it. only present the set of equations necessary to find a
solution.
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