Afurniture shop refinishes chairs. employees use one of two methods to refinish each chair. method i takes 0.5 hours and the material costs $9. method ii takes 2.5 hours, and the material costs $7. next week, they plan to spend 199 hours in labor and $1226 in material for refinishing chairs. how many chairs should they plan to refinish with each method?

method I = 88 chairs

method II = 62 chairs

Explanation:

This problem can be modeled by a system of two linear equations.

Define x as the number of chairs refinished by method I and y by method II

The sum of hours spent on both methods should equal 199 and the sum of total material cost should equal $1226, therefore:

Multiplying the first equation by -18 and adding it to the second equation we can solve for the value of y:

We can now apply the value of y found to the first equation and solve for x:

Therefore, they should refinish 88 chairs with method I and 62 chairs with method II

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .