Math 1324 Name Chapter 7 Lab 7.1-7.5 Instructions: Work each of the following problems in the space provided. You must show all work to receive full credit. Simplify and clearly indicate all answers. 1. Mellow Mushroom makes two types of pizza: basic cheese (cheese and tomatoes) and margherita (cheese, tomatoes, and basil). Mellow Mushroom sells at least 60 units a day of margherita pizza, and at least 40 units a day of the basic cheese pizza. The cost of tomatoes and basil is $2 per unit for the margherita pizza, and the cost of tomatoes is $1 per unit for the basic cheese pizza. No more than $320 per day can be spent on tomatoes and basil together. The cheese used for the margherita pizza is $5 per unit, and the cheese for the basic cheese pizza is $4 per unit. Mellow Mushroom can spend no more than $1,000 per day on cheese. How many units of each pizza should Mellow Mushroom make in order to maximize revenue if the basic cheese pizza sells for $15 per unit and the margherita pizza sells for $24 per unit? a. Clearly define the variables in this problem. x = b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. d. Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points and lines. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work. e. How many units of each pizza should Mellow Mushroom make in order to maximize revenue if the basic pizza sells for $15 per unit and the margherita pizza sells for $24 per unit?Math 1324 Name Chapter 7 Lab 7.1-7.5 Instructions: Work each of the following problems in the space provided. You must show all work to receive full credit. Simplify and clearly indicate all answers. 1. Mellow Mushroom makes two types of pizza: basic cheese (cheese and tomatoes) and margherita (cheese, tomatoes, and basil). Mellow Mushroom sells at least 60 units a day of margherita pizza, and at least 40 units a day of the basic cheese pizza. The cost of tomatoes and basil is $2 per unit for the margherita pizza, and the cost of tomatoes is $1 per unit for the basic cheese pizza. No more than $320 per day can be spent on tomatoes and basil together. The cheese used for the margherita pizza is $5 per unit, and the cheese for the basic cheese pizza is $4 per unit. Mellow Mushroom can spend no more than $1,000 per day on cheese. How many units of each pizza should Mellow Mushroom make in order to maximize revenue if the basic cheese pizza sells for $15 per unit and the margherita pizza sells for $24 per unit? a. Clearly define the variables in this problem. x = b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. d. Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points and lines. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work. e. How many units of each pizza should Mellow Mushroom make in order to maximize revenue if the basic pizza sells for $15 per unit and the margherita pizza sells for $24 per unit?\f2. On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to bring food, clothing, and other supplies to the more than 2 million people in West Berlin. The Americans had two types of planes available, the C-47 Skytrain and the C-54 Skymaster. The carrying capacity was 3.5 tons for a C-47 and 10 tons for a C-54. To break the Soviet blockade, the Western Allies had to maximize carrying capacity, but the Americans were limited by the following restrictions: . No more than 44 planes could be used per day. . Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 5. The total number of personnel available per day could not exceed 200. The Americans only had 32 C-54's available. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity. a. Define the variables. Be specific with descriptive words. b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. d. Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points and lines. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work. e. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity.2. On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to bring food, clothing, and other supplies to the more than 2 million people in West Berlin. The Americans had two types of planes available, the C-47 Skytrain and the C-54 Skymaster. The carrying capacity was 3.5 tons for a C-47 and 10 tons for a C-54. To break the Soviet blockade, the Western Allies had to maximize carrying capacity, but the Americans were limited by the following restrictions: . No more than 44 planes could be used per day. . Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 5. The total number of personnel available per day could not exceed 200. The Americans only had 32 C-54's available. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity. a. Define the variables. Be specific with descriptive words. b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. d. Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points and lines. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work. e. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity.\f3. Using the exact same problem, variables, objective function, and constraints in problem 2, solve using the Simplex Method. Show all your work, including row operations and matrices. On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to bring food, clothing, and other supplies to the more than 2 million people in West Berlin. The Americans had two types of planes available, the C-47 Skytrain and the C-54 Skymaster. The carrying capacity was 3.5 tons for a C-47 and 10 tons for a C-54. To break the Soviet blockade, the Western Allies had to maximize carrying capacity, but the Americans were limited by the following restrictions: No more than 44 planes could be used per day. Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 5. The total number of personnel available per day could not exceed 200. The Americans only had 32 C-54's available. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity. a. Convert each constraint from problem 2 into an equation by adding slack variables and set up the initial simplex matrix. b. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible. UI3. Using the exact same problem, variables, objective function, and constraints in problem 2, solve using the Simplex Method. Show all your work, including row operations and matrices. On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to bring food, clothing, and other supplies to the more than 2 million people in West Berlin. The Americans had two types of planes available, the C-47 Skytrain and the C-54 Skymaster. The carrying capacity was 3.5 tons for a C-47 and 10 tons for a C-54. To break the Soviet blockade, the Western Allies had to maximize carrying capacity, but the Americans were limited by the following restrictions: No more than 44 planes could be used per day. Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 5. The total number of personnel available per day could not exceed 200. The Americans only had 32 C-54's available. Find the number of C-47's and C-54's the Americans used to maximize their carrying capacity. a. Convert each constraint from problem 2 into an equation by adding slack variables and set up the initial simplex matrix. b. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible. UIState the number of C-47's and C-54's the Americans used to maximize their carrying capacity. d. What are the advantages/disadvantages of solving this liner programming problem using the graphing method vs. the simplex method? Justify your answer. 4. An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investment in oil leases and bonds to 30% and his investment in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables. Be specific with descriptive words. x = V= Z = b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. 6State the number of C-47's and C-54's the Americans used to maximize their carrying capacity. d. What are the advantages/disadvantages of solving this liner programming problem using the graphing method vs. the simplex method? Justify your answer. 4. An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investment in oil leases and bonds to 30% and his investment in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables. Be specific with descriptive words. x = V= Z = b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. 6d. Set up the initial simplex matrix needed to solve the linear programming problem using the Simplex Method. e. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible. f. How much should he invest in each to maximize his return, assuming investment returns are as expected?d. Set up the initial simplex matrix needed to solve the linear programming problem using the Simplex Method. e. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible. f. How much should he invest in each to maximize his return, assuming investment returns are as expected