Question

A factory manufactures widgets and grommets. Every thousand widgets use $550 worth of resources and 2 person-hours of labor. Every thousand grommets use $700 worth of resources and 6 person-hours of labor. If the factory has $47,850 woth of resources and 288 person-hours of labor available each week, how many of each product can they make? I'm confused how to solve this?

Answer 1

To solve the problem, set up a system of equations using the given information. Use substitution to solve the system and find the number of widgets and grommets that can be made.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the given information. Let's say x represents the number of thousands of widgets produced, and y represents the number of thousands of grommets produced. The cost equation can be written as: 550x + 700y = 47850, where 550 represents the cost per thousand widgets and 700 represents the cost per thousand grommets. The labor equation can be written as: 2x + 6y = 288, where 2 represents the labor required for a thousand widgets and 6 represents the labor required for a thousand grommets.

Now, we can solve this system of equations using any method of our choice, such as substitution or elimination. Let's use the substitution method. We solve the labor equation for x: 2x = 288 - 6y, x = 144 - 3y. Substituting x in the cost equation, we get: 550(144 - 3y) + 700y = 47850. Simplifying this equation, we have 79200 - 1650y + 700y = 47850. Combining like terms, we get 950y = 47850 - 79200, 950y = -31350, y = -33.

Since the number of thousands of grommets cannot be negative, we discard this solution. Therefore, we cannot make a negative number of grommets. Hence, the factory cannot produce any grommets. We can find the number of widgets by substituting y = 0 into the labor equation: 2x + 6(0) = 288, 2x = 288, x = 144. Therefore, the factory can make 144 thousand widgets.