  A company produces and sells 211,600 boxes of t-shirts each year. Each production run has a fixed cost of \$400 and an additional cost of \$3 per box of t-shirts. To store a box for a full year costs \$2. What is the optimal number of production runs the company should make each year? Do not include units with your answer.

Question

A company produces and sells 211,600 boxes of t-shirts each year. Each production run has a fixed cost of \$400 and an additional cost of \$3 per box of t-shirts. To store a box for a full year costs \$2. What is the optimal number of production runs the company should make each year? Do not include units with your answer.

Step 1

Every year, the company produces and sells 211,600 boxes of T-shirts. Each production run has a fixed cost of \$400 and an additional cost of \$3 per box of T-shirts. Let the number of production runs in a year be P. In order to obtain the optimal number of production runs, construct a cost function as follows.

Then, the number of boxes per each production run becomes

Step 2

Thus, the Cost function is constructed as

Step 3

However, there is an inventory cost of a box for a full year that is \$2.

Holding cost per year = (ave. i...

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Calculus 