Answer to Question #186861 in Economics for Abdi dhuule

Question

A company manufactures two kinds of machines, each requiring a different manufacturing technique. The deluxe machine requires 18 hours of labor, 9 hours of testing, and yields a profit of $400. The standard machine requires 3 hours of labor, 4 hours of testing, and yields a profit of $200. There are 800 hours of labor and 600 hours of testing available each month. A marketing forecast has shown the monthly demand for the standard machine to be no more than 150. Management wants to know the number of each model to produce monthly that will maximize total profit. Formulate this as a linear programming problem and solve it by using graphical method.

Answer 1

$$f(x)=400x+200y \to max$$

$$18x+3y\le800$$

$$9x+4y\le600$$

$$x\ge0, 0\le y \le150$$

x=31, y=80