Solutions and Explanations to Problems

# Solutions and Explanations to Problems - CSA 273 Solutions...

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CSA 273 Solutions to Homework #5 1 Problem #1 (a) Let x 1 = Number of units of Product 1 produced. x 2 = Number of units of Product 2 produced. P = Profit from selling x 1 units of Product 1 and x 2 units of product in dollars. The linear programming model becomes: Maximize P = 25x 1 + 30x 2 such that 1.50x 1 + 3.00x 2 450 (labor-hours availability for department A) 2.00x 1 + 1.00x 2 350 (labor-hours availability for department B) .25x 1 + .25x 2 50 (labor-hours availability for department C) x 1 ,x 2 0 (b) The constraint graph is below. Optimal solution occurs at the point of intersection of the lines defining Department A's constraint and Department C's constraint. So the system of two equations in two unknowns becomes: 1.5x 1 + 3x 2 = 450 .25x 1 + .25x 2 = 50 Solution is x 1 =100 units, x 2 =100 units. Also P=(\$25*100)+\$30*100=\$5500. Thus, the optimal solution is to produce 100 units each of Products 1 and 2 for a projected total profit contribution of \$5500. Constraint Graph for Problem 1 of HW#5 0 50 100 150 200 250 300 350 400 0 100 200 300 400 Units of Product 1 Units of Product 2 Dept A Dept B

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Solutions and Explanations to Problems - CSA 273 Solutions...

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