Question

The management of the Albert Hanson Company is trying to determine the best product mix for two new products to maximize profits. Because these products would share the same production facilities, the total number of units produced of the two products combined cannot exceed ten per hour. Also, they have to be produced in at least a two-to-one ratio, with there being at least twice as many of product 2. In particular, with a production rate of x1 units per hour, it is estimated that product 1 would provide a profit per hour of $100(x1) - $10(x1)^2 and the production rate of product 2 is x2 units per hour, its estimated profit per hour would be $300(x2) - $15(x2)^2
a) Formulate an NLP model for this problem.
b) Is the profit function concave? What does the shape of the profit function indicate about how profits change as production increases?

Answer 1

a) NLP Model

Subject to

The objective function is the profit function combined

The constraint one says that the per hour production of product 1 and per hour production of product 2 should not exceed 10

Constraint 2 says that per hour production rate of product 1 should be at least greater than twice of per hour production of product 2

The last constraint is the nonnegativity constraint

b)

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