In an economic model, the cost of production C C in terms of the number of units produced x x is given by C = 50 x + 0.02 x 2 C=50x+0.02x^2 , where C C is measured in dollars and x x in units. The linear term 50 x 50x models the fixed cost per unit, and the quadratic term 0.02 x 2 0.02x^2 models the increasing variable cost as production scales up. Find d C d x \frac{dC}{dx} at x = 100 x=100 units and describe the meaning of the derivative.

C ′ ( 100 ) = 54 C^{\prime}\left(100\right)=54 C ′ ( 100 ) = 54 If the company is currently producing 100 100 100 units and wants to increase production by 1 1 1 more unit, the additional cost would be approximately $ 54 \$54 $54 .

C ′ ( 100 ) = 54 C^{\prime}\left(100\right)=54 C ′ ( 100 ) = 54 If the company is currently producing 100 100 100 units and wants to increase production by 1 1 1 more unit, the cost would decrease by approximately $ 54 \$54 $54 .

C ′ ( 100 ) = 58 C^{\prime}\left(100\right)=58 If the company is currently producing 100 100 100 units and wants to increase production by 1 1 1 more unit, the additional cost would be approximately $ 58 \$58 .

C ′ ( 100 ) = 58 C^{\prime}\left(100\right)=58 If the company is currently producing 100 100 100 units and wants to increase production by 1 1 1 more unit, the cost would decrease by approximately $ 58 \$58 .

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Problem 71Multiple Choice

In an economic model, the cost of production $C$ in terms of the number of units produced $x$ is given by $C = 50 x + 0.02 x^{2}$ , where $C$ is measured in dollars and $x$ in units. The linear term $50 x$ models the fixed cost per unit, and the quadratic term $0.02 x squared$ models the increasing variable cost as production scales up. Find $\frac{d C}{d x}$ at $x equals 100$ units and describe the meaning of the derivative.

$C^{\prime}\left(100\right)=54$

If the company is currently producing $100$ units and wants to increase production by $1$ more unit, the additional cost would be approximately $\$54$ .

$C^{\prime}\left(100\right)=54$

If the company is currently producing $100$ units and wants to increase production by $1$ more unit, the cost would decrease by approximately $\$54$ .

$C prime of 100 equals 58$

If the company is currently producing $100$ units and wants to increase production by $1$ more unit, the additional cost would be approximately $dollar sign 58$ .

$C prime of 100 equals 58$

If the company is currently producing $100$ units and wants to increase production by $1$ more unit, the cost would decrease by approximately $dollar sign 58$ .

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