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Answer :
Therefore, the wine should be ordered 11 times a year (rounded to the nearest integer).
(a) The optimum number of bottles per order is 228. Answer more than 100 words: Let x be the number of bottles per order, then there will be (915/x) orders per year.
So, the total cost of a year would be $915 (for storage) and (915/x)(8) dollars (for orders). Therefore, the cost function C(x) is given by:
C(x)=915+(7320/x)
To find the optimum number of bottles per order we need to differentiate C(x) and equate it to zero:∂C(x)/∂x=−7320/x²
=0⇒x²
=7320⇒x
=√(7320)≈85.5
Therefore, the optimum number of bottles per order is 86 bottles.
Note that the second derivative of C(x) is positive for x > 0, so C(x) is convex upwards and, in particular, C(86) is the minimum value. So the minimum cost is: C(86)≈$1108.72
(b) The wine should be ordered (11) times a year.
To find how many times a year the wine should be ordered, we substitute x = 86 into the formula of the number of orders per year:
915/x=915/86≈10.64
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