The cost function is a quadratic. The basic form of a quadratic equation is ax^2 + bx + c = 0. You must find the values of the coefficients a, b and c.
Use the given data to construct 3 simultaneous linear equations in x:
5 = a(2)^2 + b(2) + c
143 = a(4)^2 + b(4) + c
869 = a(10)^2 + b(10) + c
You must solve for a, b and c and then write the quadratic equation
y = ax^2 + bx + c that governs the production costs. Then let x=7 and calculate y, which is the figure you want.
Using matrices, I found that a=6.5, b=30 and c=-81.
Can you now write the quadratic equation and evaluate it at x = 7?
