Cubic Cost Function

Question

Find the cost to make 22 items using the cubic cost function 1/40x^3-1.2x^2+30x+60

Answer 1

To find the cost of making 22 items using the given cubic cost function, you need to substitute x = 22 into the function and evaluate it. Here's how you can calculate it step by step:

Cost Function: C(x) = (1/40)x^3 - 1.2x^2 + 30x + 60

1. Substitute x = 22 into the cost function: C(22) = (1/40)(22^3) - 1.2(22^2) + 30(22) + 60
2. Calculate each term separately: C(22) = (1/40)(10,648) - 1.2(484) + 660 + 60
3. Perform the calculations: C(22) = (266.2) - (580.8) + 660 + 60
4. Add and subtract the values: C(22) = 266.2 - 580.8 + 660 + 60
5. Calculate the final result: C(22) = 405.4 + 660 + 60
6. Add the numbers: C(22) = 1125.4

So, the cost to make 22 items using the given cubic cost function is approximately 1125.4 units of whatever currency or cost unit is being used in this context.

Answer 2

C(22) = (1/40)22^3 -1.2(22^2) + 30(22) +60

replace x with 22 and simplify