Question

Quick Computing Company produces calculators. They have found that the cost, c(x), of making x calculators is a quadratic function in terms of x.The company also discovered that itr costs $45 to produce 2 calculators, $143 to produce 4 calculators, and $ 869 to produce 10 calculators. Find the total cost of producing 7 calculators.

PLEASE HELP ASAP

Answer 1

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?