## Figure

Feasible Space

The feasible space is reduced further by the addition of constraints on inputs B and C. Only points within the shaded region meet all constraints.

Quantity of Y (per time period)

^Constrainton input A:4QX+2QY=32

Constraint on input C: 3QY= 21 /

Constraint on input ftQx+QY=10

^Constrainton input A:4QX+2QY=32

Constraint on input C: 3QY= 21 /

Constraint on input ftQx+QY=10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity of X (per time period)

The general formula for isoprofit curves can be developed by considering the profit function n = aQX + bQY, where a and b are the profit contributions of products X and Y, respectively. Solving the isoprofit function for QY creates an equation of the following form:

Given the individual profit contributions, a and b, the QY intercept equals the profit level of the isoprofit curve divided by the profit per unit earned on QY, n/b. Slope of the objective function is given by the relative profitability of the two products, -a/b. Because the relative profitability of the products is not affected by the output level, the isoprofit curves consist of a series of parallel lines. In this example, all isoprofit curves have a slope of -12/9, or -1.33.

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