SOLUTION: Callaway Golf Company has determined that the daily cost C of manufactoring x Big-Bertha-type gold clubs may be expressed by the quadratic equation C(x)=5x^2-620x+20,000, a)How

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Question 138262: Callaway Golf Company has determined that the daily cost C of manufactoring x Big-Bertha-type gold clubs may be expressed by the quadratic equation C(x)=5x^2-620x+20,000,
a)How many clubs should be manufactured to minimize the cost?
b)At this level of production, what is the cost per club?
c)What are the fixed cost of production (the cost to produce 0 clubs)?
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Answer by solver91311(24713) About Me  (Show Source):
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Since this is a quadratic function, the graph is a parabola. Since the lead coefficient is positive, the graph opens upward. That means that the vertex of the parabola is the minimum value of the function.

To find the x-coordinate of the vertex of a a parabola f%28x%29=ax%5E2%2Bbx%2Bc, calculate x%5Bm%5D=%28-b%29%2F2a. That will give you the number of clubs to manufacture to minimize the cost.

The cost per club of that many clubs is then given by C%28x%5Bm%5D%29. In other words, substitute the value calculated in part a into the function and do the arithmetic.

The cost to produce 0, in other words, the fixed costs is given by C%280%29. Substitute 0 for x in the function and the result will be the fixed cost.