Problema Solution
The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day $4800 to produce 300 chairs in one day.
a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph.
b) What is the slope of the graph and what does it represent?
c) What is the y-intercept of the graph and what does it represent?
Answer provided by our tutors
a) let f(x) be the function that gives the cost of the chairs produced, x is the number of chairs
f(x) = ax + b, a and b are constants
we need to find a and b
f(100) = 2200
f(300) = 4800
by solving the system of equations
100a + b = 2200
300a + b = 4800
we find
a = 13
b = 900
click here to see the step by step solution of the system of equations
the function is
f(x) = 13x + 900
click here to see the graph
b) y = 13x + 900
the slope is equal to 13
slope = change in y/change in x = rise/run = (4800 - 2200)/(300 - 100) = 2600/200 = 13
the slope shows how much money is needed to produce 1 chair
c) the y-intercept is 900
it means that the start expenses of the production are $900