The managers of a business are examining costs. It is more cost-effective for them to produce more items. However, if too many items are produced, their costs will rise because of factors such as storage and overstock. Suppose that they model the cost, C, of producing n thousand items with the function C(n) = 75n2 - 1800n + 60 000. Determine the number of items produced that will minimize their costs.
+130560 C(n) =75n2 - 1800n + 60 000....if you have had Calculus, this can be determined rather quickly.....but let's assume you haven't......
This function is a parabola that turns "upward"....the quantity that will minimize the cost will be the x coordinate of the vertex (the point at the "bottom" of the curve) found by this "formula"...
x = - b/2a in our function, b = -1800 and a = 75 .....therefore.....
-(-1800)/[2(75)] = 1800/150 = 12 items
Here's the graph.......https://www.desmos.com/calculator/gzsvoswise
+130560 C(n) =75n2 - 1800n + 60 000....if you have had Calculus, this can be determined rather quickly.....but let's assume you haven't......
This function is a parabola that turns "upward"....the quantity that will minimize the cost will be the x coordinate of the vertex (the point at the "bottom" of the curve) found by this "formula"...
x = - b/2a in our function, b = -1800 and a = 75 .....therefore.....
-(-1800)/[2(75)] = 1800/150 = 12 items
Here's the graph.......https://www.desmos.com/calculator/gzsvoswise
