Answer to Question #301301 in Macroeconomics for Matt

Question

A company makes two products, A and B. Product A requires 12,5 hours of machining time and 30 minutes of finishing time per unit. Product B requires 10 hours of machining time and one hour of finishing time per unit. There are 10 000 hours and 600 hours available for machining and finishing respectively. Severe material shortages for the two products will limit their production to a maximum of 700 units for product A and 400 units for product B per day. If z and y are the number of units of product A and B produced per day respectively, choose the system of inequalities that describes the process.

1. 12,5x+10y<=10000; 0.5x + y < 600 ; x < 700 y <= 400 x, y >= 0 2. 12, 5x + 10y >= 1000 0.5x+y<600;x<700 y < 400 ; x, y >= 0 3. 12, 5x + 10y < 1000 0.5x + y <= 600 ; x > 700 ; y > 400 ; x, y > 0 4. 12, 5x + 10y < 10000 0.5x+y>=600;x>=700 y<=400; x, y > 0

Answer 1

Solution

Since the number of hours of processing materials A and B is limited to 10,000 hours, the constraint equation will be:

12,5х + 10у <=10000

For finishing time, the constraint equation is:

0,5х + 1у <=600

Due to the lack of materials for two products, two more constraint equations appear:

х<=700 and y<=400

The value of the number of units of product A and B cannot be negative, then:

х>0 and y>0

The system of inequalities that describes the process is presented in answer 1

Аnswer: 1. 12,5x+10y<=10000; 0.5x + y < 600 ; x < 700 y <= 400 x, y >= 0