54. Business: Inventory Costs Retailers are concerned about inventory costs. The total inventory cost, C(x), for a lot size of x units, is the sum of the carrying costs, H(x), and the order/reorder co...

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54. Business: Inventory Costs Retailers are concerned about inventory costs. The total inventory cost, C(x), for a lot size of x units, is the sum of the carrying costs, H(x), and the order/reorder co...

54. Business: Inventory Costs Retailers are concerned about inventory costs. The total inventory cost, C(x), for a lot size of x units, is the sum of the carrying costs, H(x), and the order/reorder costs, R(x). That is, C(x) = H(x) + R(x). All costs are in dollars.

Carrying costs are (carrying cost per unit) ⋅ x/2

Order/reorder costs are (cost per order) ⋅ (number of units sold during time period)/x

The lot size x is the number of units the company expects to sell in some time period. Approximate to 3 decimal places when necessary.

a. Construct a model for the inventory cost function when the carrying cost per unit is $4, the order/reorder cost is $15, and the company expects to sell 1,600 units over the next year.

b. Find the inventory cost when the lot size is 109 units.

c. Find the inventory cost when the lot size is 110 units.

d. Find the inventory cost when the lot size is 111 units.

e. Which of these three lot sizes produces the minimum cost?

math Advanced-Math

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54. Business: Inventory Costs Retailers are concerned about inventory costs. The total inventory cost, C(x), for a lot size of x units, is the sum of the carrying costs, H(x), and the order/reorder co...