Questions: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics processing unit). The manufacture found that the marginal cost C to produce x GPUs can be found using the equation C=0.03 x^2-4 x+900. If the marginal cost were 845, how many GPUs were produced?

A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics processing unit). The manufacture found that the marginal cost C to produce x GPUs can be found using the equation C=0.03 x^2-4 x+900. If the marginal cost were 845, how many GPUs were produced?

Transcript text: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics processing unit). The manufacture found that the marginal cost $C$ to produce $x$ GPUs can be found using the equation $C=0.03 x^{2}-4 x+900$. If the marginal cost were $\$ 845$, how many GPUs were produced? $\square$ Select an answer

Solution

Solution Steps

Step 1: Start with the given equation \(C = ax^2 - bx + c\).

Substitute the given value of \(C\): \(C = 845\) into the equation to get \(ax^2 - bx + (c - C) = 0\).

Step 2: Rearrange the equation to form a standard quadratic equation.

The adjusted equation is \(ax^2 - bx + (55) = 0\).

Step 3: Calculate the discriminant \(D = b^2 - 4ac'\).

For our parameters, \(D = -4^2 - 4_0.03_55 = 9.4\).

Since \(D > 0\), there are two distinct real solutions for \(x\).

Step 4: Solve the quadratic equation using the formula \(x = \frac{{-b \pm \sqrt{{D}}}}{{2a}}\).

The solutions are \(x_1 = 117.766\) and \(x_2 = 15.568\).

Step 5: Choose the positive, realistic solution.

The number of GPUs produced, rounded to 2 decimal places, is 15.57.

Final Answer:

The number of GPUs that can be produced is 15.57, given the marginal cost \(C = 845\).

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