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Given the Total Cost function:

Computer Science

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5 parts
i
60
ii

x2+60xx^2 + 60x

iii

x+60+60xx + 60 + \frac{60}{x}

iv

x + 60

v

2x + 60

Given the Total Cost function:

TC=x2+60x+60TC = x^2 + 60x + 60

i) Fixed Cost (FC)
Fixed cost is the portion of total cost that does not vary with the level of output (xx). It is the constant term in the total cost function.

FC=60FC = 60

The fixed cost is 60\boxed{60}.

ii) Variable Cost (VC)
Variable cost is the portion of total cost that changes with the level of output (xx). It includes all terms in the total cost function that contain xx.

VC=x2+60xVC = x^2 + 60x

The variable cost is x2+60x\boxed{x^2 + 60x}.

iii) Average Total Cost (ATC)
Average total cost is the total cost per unit of output. It is calculated by dividing the total cost by the quantity of output (xx).

ATC=TCxATC = \frac{TC}{x} ATC=x2+60x+60xATC = \frac{x^2 + 60x + 60}{x} ATC=x2x+60xx+60xATC = \frac{x^2}{x} + \frac{60x}{x} + \frac{60}{x} ATC=x+60+60xATC = x + 60 + \frac{60}{x}

The average total cost is x+60+60x\boxed{x + 60 + \frac{60}{x}}.

iv) Average Variable Cost (AVC)
Average variable cost is the variable cost per unit of output. It is calculated by dividing the variable cost by the quantity of output (xx).

AVC=VCxAVC = \frac{VC}{x} AVC=x2+60xxAVC = \frac{x^2 + 60x}{x} AVC=x2x+60xxAVC = \frac{x^2}{x} + \frac{60x}{x} AVC=x+60AVC = x + 60

The average variable cost is x+60\boxed{x + 60}.

v) Marginal Cost (MC)
Marginal cost is the additional cost incurred by producing one more unit of output. It is calculated as the derivative of the total cost function with respect to xx.

MC=d(TC)dxMC = \frac{d(TC)}{dx}

Given TC=x2+60x+60TC = x^2 + 60x + 60.

MC=ddx(x2+60x+60)MC = \frac{d}{dx}(x^2 + 60x + 60) MC=2x+60+0MC = 2x + 60 + 0 MC=2x+60MC = 2x + 60

The marginal cost is 2x+60\boxed{2x + 60}.

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