A service sells an item at a constant rate the $r$ devices per month. It reorders in batches that $q$ units, in ~ a price of $a+b q$ dollars per order. Storage prices are $k$ dollars per item every month, and, on average, $q / 2$ items room in storage, waiting to be sold. (a) How regularly does the business reorder?(b) What is the typical monthly cost of reordering?(c) What is the total monthly cost, $C$ of ordering and storage?(d) attain Wilson's lot size formula, the optimal batch size which minimizes cost.

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Oh, this is a problem around business marketing item A constant rate off our systems for month on its reorders in batches off kids. For this reason a reorder complain skewed, and the expenses of reordering is a plus. Begin, they close. Start storage costs. Story is offering us que doors Paraiso. Okay, Those her Arthur the promoter. Every right. And the leverage. Ah. Huh. Room in storage wait to assault. Okay. Questioning just how awful. How awful the reordering things, please. Right thing. When do we have actually re order? Well, us should, as we market a certain variety of units every month, then our reordering should keep pace. V that. We'll fail. Therefore we're going to say how much will offered in. Let's see, three months time Thio offered month, uh, at any time it have to be equal to the er just how much was reordered reorder in those females? all right, so us calculate the values recalculate time to express time v the letter C. Currently let's view if us so debates promote. Climate we have actually our tea r t offered in Simmons. Oh, from guarantee is for this reason in 3 months. And also how much was reordered? Reorder Q. Friend know, it's okay. So each month us reorder. Q. You are the bar here. We perform our through our cube bar the this offers us an expression. How countless months? Uh, pass? This might be a portion more 0.3. Be ordering every ripe days. Basically, this ratio he acute through our where Q is the, uh, read order number Unis on our is the number of Ian. For this reason let's cue with her cool wish being is the median monthly course. Oh, reordering. What is it? Okay, for this reason what is the price of one reorder the expense of one reorder is April speak right here on and also the variety of months Is her gun here? Cute through space so really by these two to uncover what the median cough booth this'd is able to do you a large queue v one split by this way multiplied by our skiing way have ours A add to barbecue for a son which we can write us space a kid plus the army. You will certainly cancel right here right That we heard? Yes, with me. Ghoulish c you have to see asks because that what is the complete mostly cost. Uh, as soon as we have both ordering plus ah, story. Okay. We found that the mean monthly price is, uh, are a v pure plus R B on DDE. The storage expenses are cake you, however there we have actually it. That's the thing. Question. Perm point asks human being use ruthless conference people optimum optimal batch dimension that, uh, minimizes walk Oh, we won't watch a CZ role of Q to be minimal So us find an essential points What is the flow to the sea in terms we different traits This law right here we'll rewrite the sea duty c equals R a Q to the minus an initial K through secu add to r B. I'm simply really well, this formula here Yes, we have the right to differently. Therefore this will be minus one time ar e minus R A Q to the mind of a 2nd This will certainly be plus caher top top R B has actually no que in the regards to this constant and is the root is zero in terms of So we want the derivative off Q V 0 to 5 vital parts. The transfer this to the various other side k equals, uh space a through cute that weird therefore we'll popular music you squared up cable go down to go up que square will be su r a over. Okay. So taking square root curie holes skirt to our A because that room. Okay. Since three or a batch, dimension is an essential units way. We discovered the an adverse solution. He is. The is only one crucial point for view on dhe It have to there it is in the minimal. And there we have actually it. Have actually we come? various other name oppression the we check out a B c d.

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