Inquiry Question Can I determine whether the hamburger or the quarter pounder with cheese makes McDonald's more money? Name: Date: Quarter Pounder cheese that M General Instructions McDonald's first came out with their basic hamburger in 1948 and the quarter pounder in 1973. These burgers have been around for a while, but does one of them make more profit than the other? Questions like this are asking us to optimize the profit to determine what combination of sales of these burgers makes the most money. You will use inequalities to investigate how selling different amounts of each burger affects profit at a specific restaurant. Your task is to determine if the hamburger, the quarter pounder with cheese, or some combination of the two brings in more profit for this specific restaurant. Materials you'll need: Pencil, eraser, calculator, computer. Cerner TON STATES OOT WATER 82 ARA GOSE DE VERE E PORTA 35 ONALANIZZA Determining the System of Inequalities The question to investigate is this: is the hamburger or the quarter pounder with cheese more profitable? More specifically, what combination of sales of these burgers leads to the most profit? Is it only selling quarter pounders? How about selling 500 of each? This is our challenge to investigate. Let's look at this scenario (The numbers used are reasonable and give some idea of how each burger affects profits): A McDonald's restaurant sells many food items, but as the financial analyst for McDonald's in this region, your task is to determine if the hamburger, the quarter pounder with cheese, or some combination of the two brings in more profit for this specific restaurant on an average day. You must consider cost to make each burger, the sell price, the efficiency in producing both burgers, how many burgers are available, and available time. This McDonald's will make up to and including 1000 hamburgers and quarter pounders in total in a day. It takes a certain number of seconds to grill and prepare these burgers, and you have this information with you from McDonald's corporate: How long does it take to cook a burger on the grill? This varies from one sandwich to another and depends on how many orders have been placed at one time. As an example, if there are no other orders, the average time from when an order is placed to cook and prepare a Hamburger is a total of 112 seconds (the beef patty is cooked on the grill in 42 seconds) and a total of 180 seconds for a Quarter Pounder with Cheese (the beef patty is cooked on the grill in 112 seconds). In a day, 5 grill employees will work a full 8-hour shift each to complete these burger orders. There is no limit to the number of hamburgers that can be made a day, but a maximum of 600 quarter pounders can be made. Let's build the system of inequalities (constraints) that will allow us to answer our question. Let x = # of hamburgers, y = # of quarter pounders with cheese. 1. What are the inequalities that restrict how many of each burger can be made? Write all 3 of them below. 2. What is the inequality that governs the amount of time available to make the burgers? Show your thinking. Use the information in the scenario to build an inequality that fits this structure: time to make a hamburger + time to make a Q.P. total time available for all workers Determining the Objective Equation Now that we have our inequalities, how can we calculate the profit? We need to know how much it costs to make each burger and how much they sell for. Research how much each burger costs to purchase in your area (include a picture of the prices) and use the table below to determine how much it costs to make each burger. REGULAR MENU Angus Bacon & Cheese $ 2.10 8568 8562 What is the objective equation that describes profit on burgers sold? Show your thinking. Mighty Angus $ 2.24 5 Big Mac $ 1.14 410 Double Big Mac $ 1.82 3 Cheeseburger $ 0.59 4 Double Cheeseburger $ 1.05 2 Double Hamburger $ 0.82 8 Filet $0.98 4132 Double Filet $0.96 1416 Grilled Cheese $ 0.40 1 Hamburger $ 0.48 3133 Junior Chicken $ 0.49 7734 Bacon Ranch Jr Chkn $ 0.73 7094 Bacon McDouble $ 1.12 9 McChicken $ 0.73 4139 McDouble $0.93 7 Quarter Cheese $ 1.29 370 Double Quarter Chs $ 2.15 6298 Quarter Cheese BLT $ 1.67 6776 DBL Qtr BLT $ 2.53 10565 Cottage Country Crispy $1.67 10573 Cottage Country Grill $ 1.87 11432 Potato Rosti Burger $ 1.61 Graphing Write all the inequalities and equations you determined in the box. System of Inequalities and Objective Equation Graph each system using Desmos. Include a screenshot of your graph with all vertices visible. Write the vertices in the table below. X y Optimizing Profit As a reminder, the question we are investigating is this: what combination of sales of each burger leads to the most profit? Answer this question by using the objective equation and the vertices to determine which values of x and y give the highest profits. Show all your work. Questions 1. What if it took twice the cook/prep time to make a quarter pounder with cheese? How would this affect which combination of burger sales makes the most profit? Justify your answer and include graphs and calculations if necessary. 2. If the maximum number of burgers that could be made in a day was different, how would this affect which combination of burger sales makes the most profit? Investigate a new maximum of 500 burgers or 1500 burgers. Include screenshots of your graph and any calculations. Inquiry Question Can I determine whether the hamburger or the quarter pounder with cheese makes McDonald's more money? Name: Date: Quarter Pounder cheese that M General Instructions McDonald's first came out with their basic hamburger in 1948 and the quarter pounder in 1973. These burgers have been around for a while, but does one of them make more profit than the other? Questions like this are asking us to optimize the profit to determine what combination of sales of these burgers makes the most money. You will use inequalities to investigate how selling different amounts of each burger affects profit at a specific restaurant. Your task is to determine if the hamburger, the quarter pounder with cheese, or some combination of the two brings in more profit for this specific restaurant. Materials you'll need: Pencil, eraser, calculator, computer. Cerner TON STATES OOT WATER 82 ARA GOSE DE VERE E PORTA 35 ONALANIZZA Determining the System of Inequalities The question to investigate is this: is the hamburger or the quarter pounder with cheese more profitable? More specifically, what combination of sales of these burgers leads to the most profit? Is it only selling quarter pounders? How about selling 500 of each? This is our challenge to investigate. Let's look at this scenario (The numbers used are reasonable and give some idea of how each burger affects profits): A McDonald's restaurant sells many food items, but as the financial analyst for McDonald's in this region, your task is to determine if the hamburger, the quarter pounder with cheese, or some combination of the two brings in more profit for this specific restaurant on an average day. You must consider cost to make each burger, the sell price, the efficiency in producing both burgers, how many burgers are available, and available time. This McDonald's will make up to and including 1000 hamburgers and quarter pounders in total in a day. It takes a certain number of seconds to grill and prepare these burgers, and you have this information with you from McDonald's corporate: How long does it take to cook a burger on the grill? This varies from one sandwich to another and depends on how many orders have been placed at one time. As an example, if there are no other orders, the average time from when an order is placed to cook and prepare a Hamburger is a total of 112 seconds (the beef patty is cooked on the grill in 42 seconds) and a total of 180 seconds for a Quarter Pounder with Cheese (the beef patty is cooked on the grill in 112 seconds). In a day, 5 grill employees will work a full 8-hour shift each to complete these burger orders. There is no limit to the number of hamburgers that can be made a day, but a maximum of 600 quarter pounders can be made. Let's build the system of inequalities (constraints) that will allow us to answer our question. Let x = # of hamburgers, y = # of quarter pounders with cheese. 1. What are the inequalities that restrict how many of each burger can be made? Write all 3 of them below. 2. What is the inequality that governs the amount of time available to make the burgers? Show your thinking. Use the information in the scenario to build an inequality that fits this structure: time to make a hamburger + time to make a Q.P. total time available for all workers Determining the Objective Equation Now that we have our inequalities, how can we calculate the profit? We need to know how much it costs to make each burger and how much they sell for. Research how much each burger costs to purchase in your area (include a picture of the prices) and use the table below to determine how much it costs to make each burger. REGULAR MENU Angus Bacon & Cheese $ 2.10 8568 8562 What is the objective equation that describes profit on burgers sold? Show your thinking. Mighty Angus $ 2.24 5 Big Mac $ 1.14 410 Double Big Mac $ 1.82 3 Cheeseburger $ 0.59 4 Double Cheeseburger $ 1.05 2 Double Hamburger $ 0.82 8 Filet $0.98 4132 Double Filet $0.96 1416 Grilled Cheese $ 0.40 1 Hamburger $ 0.48 3133 Junior Chicken $ 0.49 7734 Bacon Ranch Jr Chkn $ 0.73 7094 Bacon McDouble $ 1.12 9 McChicken $ 0.73 4139 McDouble $0.93 7 Quarter Cheese $ 1.29 370 Double Quarter Chs $ 2.15 6298 Quarter Cheese BLT $ 1.67 6776 DBL Qtr BLT $ 2.53 10565 Cottage Country Crispy $1.67 10573 Cottage Country Grill $ 1.87 11432 Potato Rosti Burger $ 1.61 Graphing Write all the inequalities and equations you determined in the box. System of Inequalities and Objective Equation Graph each system using Desmos. Include a screenshot of your graph with all vertices visible. Write the vertices in the table below. X y Optimizing Profit As a reminder, the question we are investigating is this: what combination of sales of each burger leads to the most profit? Answer this question by using the objective equation and the vertices to determine which values of x and y give the highest profits. Show all your work. Questions 1. What if it took twice the cook/prep time to make a quarter pounder with cheese? How would this affect which combination of burger sales makes the most profit? Justify your answer and include graphs and calculations if necessary. 2. If the maximum number of burgers that could be made in a day was different, how would this affect which combination of burger sales makes the most profit? Investigate a new maximum of 500 burgers or 1500 burgers. Include screenshots of your graph and any calculations