I first posted this in the business forum (http://www.freemathhelp.com/forum/threads/95383-Real-life-problem-projecting-sales-for-shrimp), but a customer/math teacher clued me in that this could be a chi square or goodness of fit problem. I was horrible at statistics and don't remember either approach. Therefore, I was hoping someone(s) could help me out here. A quick background to the problem: I run an indoor shrimp growing company. Shrimp come to us at miniscule size and we grow them to sellable sizes. I need to come up with a projection of sales for the next six months for one batch of shrimp. I don't need a perfect answer, so I've simplified the problem below as much as I can.
The batch in question will have 30 thousand shrimp. Presume none of them die during production. Presume that they start at exactly the same mass and grow at exactly the same rate. Presume that the batch will sell out entirely in the end. Furthermore, presume that I will only sell shrimp from the batch at four exact mass milestones: 1/35 lb each (size "small") ; 1/27 lb each (size "medium") ; 1/22 lb each (size "large") ; 1/16 lb each (size "jumbo").
Here's where things get too tricky for me. Using actual past sales figures, I can reasonably project that 23% of the pounds (not pieces of shrimp) sold will be "small" pounds ; 42% will be "medium" pounds ; 23% will be "large" pounds ; and 12% will be "jumbo" pounds. I somehow need to use this percentage information to figure out the actual number of pounds of small I will sell, the actual number of pounds of medium, the actual number of pounds of large, and the actual number of pounds of jumbo.
If it's important in thinking through the problem, keep in mind that the four parts of the batch will be sold off at four different times. At the small size milestone, I'll sell from the batch until there are no more takers. The population of the batch will go down, and on the way to the next milestone, the remaining individuals in the batch will gain mass. This process repeats at the medium, large, and jumbo milestones.
This would be a simple problem if I knew the total poundage of all the shrimp sold in the batch, but I'm lacking that important bit of info.
The batch in question will have 30 thousand shrimp. Presume none of them die during production. Presume that they start at exactly the same mass and grow at exactly the same rate. Presume that the batch will sell out entirely in the end. Furthermore, presume that I will only sell shrimp from the batch at four exact mass milestones: 1/35 lb each (size "small") ; 1/27 lb each (size "medium") ; 1/22 lb each (size "large") ; 1/16 lb each (size "jumbo").
Here's where things get too tricky for me. Using actual past sales figures, I can reasonably project that 23% of the pounds (not pieces of shrimp) sold will be "small" pounds ; 42% will be "medium" pounds ; 23% will be "large" pounds ; and 12% will be "jumbo" pounds. I somehow need to use this percentage information to figure out the actual number of pounds of small I will sell, the actual number of pounds of medium, the actual number of pounds of large, and the actual number of pounds of jumbo.
If it's important in thinking through the problem, keep in mind that the four parts of the batch will be sold off at four different times. At the small size milestone, I'll sell from the batch until there are no more takers. The population of the batch will go down, and on the way to the next milestone, the remaining individuals in the batch will gain mass. This process repeats at the medium, large, and jumbo milestones.
This would be a simple problem if I knew the total poundage of all the shrimp sold in the batch, but I'm lacking that important bit of info.
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