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How Many Hamburgers?

While Charlie is out of the shop, a local meat vendor calls and asks to speak to the manager of Brubaker's Grill regarding a money saving deal he can offer on hamburger meat. Joe is excited to talk with the vendor. He is anxious to prove to Charlie that he can be a manager, so he arranges a meeting with the vendor to explore the offer. The deal, as proposed by the vendor, would require Brubaker's to buy a lot of hamburgers, but the price per patty sounds very attractive. Joe listens to the proposal and wonders if this offer is worth pursuing, given their historical rate of hamburger usage and the prices per patty that they are currently paying.

The data:
Charlie sells around 12 cases of hamburgers weekly.
Each case contains 80 hamburgers
Each hamburger patty costs $.60

New vender offer is:
Week 1 order: 50 cases at $.30 per patty
Then 15 cases for the next 12 weeks at $.45 per patty

1. How many hamburgers does Charlie normally sell during the period of the contract?
2. What is the total cost of the hamburger inventory for the period?
3. How many hamburgers will Charlie need to purchase under the new vendor contract?
4. What is the total cost of this inventory?
5. What is the average cost of a hamburger under this deal? (Round to the nearest cent.)
6. What is the percent savings per hamburger under the new deal?
7. What is the total cost savings? If Charlie accepts the new deal, rather than buying the same amount of burgers from his current vendor, what is the total cost savings?
8. If hamburger sales remain stable at 12 cases per week during this period, how many hamburgers will Charlie have remaining in inventory at the end of 13 weeks?
9. If hamburger sales remain stable at 12 cases per week into the future, how many weeks will it take to sell the remaining hamburgers? (Round to the nearest week.)
10. If Joe can figure out a way to sell 14 cases a week, how many weeks will it take to sell the entire new vendor inventory? (Round to the nearest week.)
11. Beyond the price per patty savings, what factors should Joe consider when advising Charlie whether or not to take the new deal?
12. The price per patty quoted by the new vendor is attractive, but is this a good deal for the restaurant?
13. Beyond the cost savings, what other factors need to be considered before buying a lot more hamburgers than you have sold in the past?
14. How can Joe make this deal more attractive to Charlie?

"How Many Hamburgers:"

Solution Preview

The best thing to do in these types of problems is to read the prompt carefully and write down all of the important numbers given to you as well as their labels. While reading the prompt, I wrote down:
Normal: 12 cases/week, 1 case = 80 burgers, costs 0.60 /burger
Offer : Week 1 - 50 cases @ 0.30/ burger
Next 12 weeks - 15 cases @ 0.45/ burger

1. Contract covers 13 weeks (Special week 1 and 12 additional weeks). Normally Charlie sells (13 weeks)*(12 cases / 1 week)*(80 burgers / case)= 12480 burgers in 13 weeks
2. Over this period each burger costs 0.60 and there are 12480 burgers. .6*12480 = $7488
3. During the vendor contract: Add number of burgers in week 1 and number of burgers for each of the additional 12 weeks.
Week 1 : = (50 cases)*(80 burgers/ case) = 4000 ...

Solution Summary

The expert determines how many hamburgers a vendor can call.