Minimize inventory​ costs

[viathanmk1]

I am lost on how to solve this word problem. I know it has something to do with the cost function, but I am not sure what to do with it. I read somewhere that you should see the cost function as y=mx+b and find the slope of the two points, but I could not follow what they were saying. What is the best way to tackle this problem?

Cost Function: C(x)=ax+b

Question:
A retail outlet for calculators sells 800 calculators per year. It costs ​$2 to store one calculator for a year. To​ reorder, there is a fixed cost of $8​,plus $1.25 for each calculator. How many times per year should the store order​ calculators, and in what lot​ size, in order to minimize inventory​ costs?

The Store should order ___ calculators ___ times per year to minimize inventory costs.

 

[stapel]

I am lost on how to solve this word problem. I know it has something to do with the cost function, but I am not sure what to do with it. I read somewhere that you should see the cost function as y=mx+b and find the slope of the two points, but I could not follow what they were saying.

Why not ask "them" what "they" meant? (We don't know who you've been talking to, so we can't really help you with this part.)

What is the best way to tackle this problem?

Start by using what you learned back in algebra, and then applying what you're learning now in calculus.

Cost Function: C(x)=ax+b

Is this part of the exercise?

Question:
A retail outlet for calculators sells 800 calculators per year. It costs ​$2 to store one calculator for a year. To​ reorder, there is a fixed cost of $8​,plus $1.25 for each calculator. How many times per year should the store order​ calculators, and in what lot​ size, in order to minimize inventory​ costs?

They've asked you to find two different pieces of information: the order size, and the number of orders. They've given you the storage costs and the ordering costs; the ordering cost is the sum of a fixed charge (for shipping, maybe) and the per-item wholesale cost.

The per-item cost doesn't change based on order size or order frequency. The fixed charge doesn't change with order size, but the more orders you place (for instance, ten orders of eighty units, rather than eight orders of a hundred units), the more you'll pay for shipping. So this is something you'll want to minimize.

The storage costs are fixed for each unit. You'd like to minimize storage costs, but you don't want to keep inventory way low, so that you're making many small orders; at some point, you'd be paying more in shipping than you'd be saving in storage. So this is something that you'll need to balance.

Assuming that consumption is "smooth" (that is, at a consistent rate throughout the year), you'll be selling 800 units over the course of the year. You're starting the year with "c" calculator units. Let "t" stand for the fraction of the year which has passed so far (so, for instance, "six months" is "t = 0.5"). Using these variables and the explanation to a similar exercise found (here), can you get started?