Optimizing Box Sales for Maximum Profit: A Case Study in Business Strategy

[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

company expenses = $4000 monthly

This isn't a HOMEWORK question so I didn't want to put it in that section. Just something I came across in class and it greatly intrigued me because I could not make heads or tails of where to start

all help is appreciated guys!

 

[symbolipoint]

Must one assume the customer will buy the minimum required for any plan? That condition allows you to compute the total profit for each plan. The result will be obvious.

 

[currysohot]

yes the customer buys the minimum for any plan. but that is the MINIMUM. they can potentially commit to more. so they might be on the plan to buy a minimum 50 boxes but they might be getting 75 boxes a month...along those lines. that's why it said what plan and what volume (both of plans and the amount of boxes included within the plan) will give optimum profit. plus I know conditionally one can just compare profits straight away...but I believe it needs furthur delving into

 

[symbolipoint]

The profit on each box in each plan are already a known constants, so the cost to the customer is not important.

Letting x be the number of boxes, r is the profit,
Plan 1: r=20*x
plan 2: r=15*x+20*15
plan 3: r=10*x+50*10

Now I noticed your condition that company has $4000 allowed monthly expenses.

Is this the right understanding of your question: The customer buys a box, as example plan 1, for $50, and then $20 is the profit and the remaining $30 is for price of supply of the box and other company expenses?

 

[currysohot]

yeah I forgot to add the expenses part earlier. I only noticed after your reply. The company is supposed to be meeting its expenses from the profit made for each box and then make a further profit after clearing their $4000 monthly expenses

 

[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!

 

[coolul007]

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

 

[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.

 

[symbolipoint]

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

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.

 

[symbolipoint]

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!

Currysohot,
Do you have more details about this boxes & plans idea?

 

[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.

 

[berkeman]

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

company expenses = $4000 monthly

This isn't a HOMEWORK question so I didn't want to put it in that section. Just something I came across in class and it greatly intrigued me because I could not make heads or tails of where to start

all help is appreciated guys!

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.

 

[symbolipoint]

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.

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

 

[berkeman]

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

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

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?

 

[berkeman]

Thread unlocked.

 

[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

 

[berkeman]

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

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

https://www.physicsforums.com/showthread.php?t=373889

You will get fine help in the HH forums. And thank you for any clarifications you can provide on the problem.