Dana Morales and Brandon Nguyen are good friends and they decided to open a gourmet dessert place in the town where they grew up in. Dana’s family owns a building in downtown and agreed to let them use the place free of charge for a year. Dana and Brandon have no idea what type of dessert to offer and decided to focus on chocolate products. Dana and Brandon knew that they have to determine how many desserts to prepare every night so they can stock up. Based on their initial research, they estimated that they could sell about 60 servings of chocolate-based dessert every night. While they are still determining the right number and type of desserts to offer, Dana and Brandon decided to offer a hot and a cold chocolate dessert to start. Each hot chocolate dessert requires 15 minutes to prepare. The cold chocolate dessert takes twice as long. Kitchen staff labor is available daily for 20 hours. Because winter is coming, Dana and Brandon estimates that they will sell at least three hot chocolate desserts for every two cold chocolate desserts. However, they also estimated that at least 10% of their clientele would order cold chocolate desserts. The profit from each hot chocolate dessert is about $12. They estimate to gain $16 for every order of cold chocolate dessert. Instructions: 1) Formulate the complete LP model to help Dana and Brandon estimate the number of servings they should prepare each night. 2) Solve this problem graphically and show your graph with the feasible solution area (hand-drawn or digital graphs are okay). 3) If Dana and Brandon increase the profit of the hot chocolate dessert to match the cold chocolate dessert, discuss the impact on the optimal solution. 4) Discuss the effect this would have on the preparation plan, if instead of the estimated 10% of clientele would order cold chocolate dessert, it is now 20%. 5) Dana and Brandon are considering investing in some marketing to increase the number of clients. They allocated $30 a day to spend on promotions. They feel that if they do this, it will increase their orders from 60-70. Should they invest? Explain your answer. 6) Dana and Brandon are concerned with the new team. Some of them are college kids who may not need the work. They estimate that on some days, they can reduce the number of hours by 5 hours. Discuss how this will have an impact on their profits.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Dana and Brandon have no idea what type of dessert to offer and decided to focus on chocolate products. Dana and Brandon knew that they have to determine how many desserts to prepare every night so they can stock up. Based on their initial research, they estimated that they could sell about 60 servings of chocolate-based dessert every night. While they are still determining the right number and type of desserts to offer, Dana and Brandon decided to offer a hot and a cold chocolate dessert to start. Each hot chocolate dessert requires 15 minutes to prepare. The cold chocolate dessert takes twice as long.
Kitchen staff labor is available daily for 20 hours. Because winter is coming, Dana and Brandon estimates that they will sell at least three hot chocolate desserts for every two cold chocolate desserts. However, they also estimated that at least 10% of their clientele would order cold chocolate desserts. The profit from each hot chocolate dessert is about $12. They estimate to gain $16 for every order of cold chocolate dessert.
Instructions:
1) Formulate the complete LP model to help Dana and Brandon estimate the number of servings they should prepare each night.
2) Solve this problem graphically and show your graph with the feasible solution area (hand-drawn or digital graphs are okay).
3) If Dana and Brandon increase the profit of the hot chocolate dessert to match the cold chocolate dessert, discuss the impact on the optimal solution.
4) Discuss the effect this would have on the preparation plan, if instead of the estimated 10% of clientele would order cold chocolate dessert, it is now 20%.
5) Dana and Brandon are considering investing in some marketing to increase the number of clients. They allocated $30 a day to spend on promotions. They feel that if they do this, it will increase their orders from 60-70. Should they invest? Explain your answer.
6) Dana and Brandon are concerned with the new team. Some of them are college kids who may not need the work. They estimate that on some days, they can reduce the number of hours by 5 hours. Discuss how this will have an impact on their profits.
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