# Help with strange question

1. Jan 7, 2013

### currysohot

Hi we had this strange question come up in our advanced class and I'm quite confused as to how to go about figuring this one out. Here is the situation of a question

A company sells boxes to its customers but recently the company has been struggling to make a profit. Looking at the plans they offer to their clients below determine which plan and what volume of boxes need to be sold to achieve OPTIMUM profit in 6 months time. Can you develop a similar plan to furthur increase company profits?

Box plan 1 - Box cost to customer - $50, Profit on box -$20, customer must buy no minimum buy amount per month (5 boxes per transaction minimum buy however)
Box plan 2 - Box cost to customer - $45, Profit on box -$15, customer must buy minimum 20 boxes per month
Box plan 3 - Box cost to customer - $40, Profit on box -$10, customer must buy minimum 50 boxes per month

6. Jan 8, 2013

### HallsofIvy

So the $30 is the cost of making each box and the$4000 monthly cost is additional? Then the "cost to customer" is irrelevant. You can throw the first scenario out immediately. You are guarenteed no more than a net $100 which certainly won't meet your$4000 expenses! At $15 profit per box, 20 boxes per month, you will net$300 per month- still not meeting your $4000 cost. At$10 profit per box, 50 boxes per month you will net $500 per month, still no where near your$4000 monthly costs.

Unless there is some other information you haven't told us, you are doomed!

7. Jan 8, 2013

### coolul007

This looks like linear programming and the result is supposed to be the number of customers for each plan, just a guess.

8. Jan 8, 2013

### hddd123456789

From a business-perspective, it's pretty straightforward I think. It costs money to make the boxes, the profit is the amount made on selling each box minus this cost. The monthly expenses are clearly then the other operating expenses (i.e. rent, utilities, supplies, servicing, etc).

So the question is asking what ratio, plan1:plan2:plan3, of each plan should be sold each month such that total sales of all the plans minus the monthly expenses of \$4000 would the greatest. I think.

But I'm not sure that this ratio would be constant. Which ratio of plans to sell producing the largest possible profit likely depends on the overall volume of sales at the moment.

9. Jan 8, 2013

### symbolipoint

The original questions was restricted to "Which plan?", not asking for what combination of plans or number of boxes or customers among a combination of plans.

10. Jan 8, 2013

### symbolipoint

Currysohot,

11. Jan 8, 2013

### haruspex

There's no mention of demand. If there's no demand there are no sales of boxes or plans, so they're all doomed. If there's plenty of demand then take the largest profit per box. The 'minimum boxes per month' deals can only be beneficial if they result in some customers buying more boxes than they need.

12. Jan 8, 2013

### Staff: Mentor

It is *SCHOOLWORK* and you posted with no effort shown, hoping that others would do your work for you. Good job. Check your PMs.

Thread is moved to HH and locked.

13. Jan 8, 2013

### symbolipoint

Doubtful, as currysohot said it was just something he thought about, and the problem description seems missing something.

14. Jan 9, 2013

### Staff: Mentor

Something he thought about because it came up in class. That would be schoolwork, no? Thanks for doing his homework for him. Boosted his grade on this assignment pretty well. And he is prepared to do well on his future assignments how?

15. Jan 9, 2013

### Staff: Mentor

16. Jan 10, 2013

### currysohot

to be edited fully when I get back

but this is NOT a homework question. the class has moved far past this. I am simply very intrigued by it. I went back to check with my teacher again today after reading some of the responses and I had inf act missed out some key points. I'll be updating them as soon as I return.

Thanks for unlocking. Please also remove my warning

Last edited: Jan 10, 2013
17. Jan 11, 2013

### Staff: Mentor

We treat all schoolwork the same here on the PF. Please check out this thread for an explanation: