7 If it costs a company 5000 to produce 500 widgets and 1500

7. If it costs a company $5,000 to produce 500 widgets and $15,000 to produce 10,000 widgets, find the linear cost function

Let the cost be y and number of widgest be x

Then the equations are

5000 = 500x + C ----- (i)

15000 = 10000x + C ----- (ii)

subtracting equation (i) from equation (ii) we get

10000 = 9500x

x = 10000/9500 = 1.0526315

substiuting in the first equation we get

C = 5000 - 500(1.0526315) = 4473.68

Linear cost function for x widgets will be

y = 1.0526315x + 4473.68