here is the project :

[A northern hardware company is studying a plan to open a new distribution center in southeast. The company plans to rent a warehouse and an adjacent office and distribute its main products to the local dealers. The company has decided to initially start with four of its main products: Pressure washers, Go karts, Generators, and Water pumps. The table below describes how much each of the products will cost the company (including transportation costs):

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Item Cost (in Dollars)

Pressure washer 330

Go-kart 370

Generator 410

(Case of 5 Water Pumps) 635

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The company has set aside a purchasing monthly budget of $170,000 for the new location. The selling prices (per unit) for each item are given in the table below:

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Item Selling Price (in Dollars)

Pressure washer 499.99

Go-kart 729.99

Generator 700.99

Water pump 269.99

___________________________

Other than the budget, another of the company's concern is the available space in the warehouse. The warehouse has 82 shelves, and each shelf is 30 ft long and 5 ft wide. Pressure washers and generators each are stored on 5 ft by 5 ft pallets whereas each Go Kart is stored on an 8 ft by 5 ft pallet. Furthermore, a 5 ft by 5 ft pallet is used to store four cases of water pumps. For promoting its brand products, the company's marketing department has decided to allocate at least 30% of its inventory to pressure washers and Go Karts and sell at least twice as many generators as water pumps.]

now, Perform a monthly analysis using a linear programming model to maximize the company's net profit.

Use the Python Solver solve the problem, and generate a sensitivity report.

I did the first part to solve the problem like follow :

[# Set up the linear programming formulation import pulp

# Create a maximization problem object problem = pulp.LpProblem('Northern Hardware Problem', pulp.LpMaximize)

# Define decision variables x1 = pulp.LpVariable('Pressure Washers', lowBound=0, cat='Integer') x2 = pulp.LpVariable('Go Karts', lowBound=0, cat='Integer') x3 = pulp.LpVariable('Generators', lowBound=0, cat='Integer') x4 = pulp.LpVariable('Cases of Water Pumps', lowBound=0, cat='Integer')

# Define objective function problem += (499.99 - 330) * x1 + (729.99 - 370) * x2 + (700.99 - 410) * x3 + (269.99 - 635/4) * x4

# Add constraints problem += 330*x1 + 370*x2 + 410*x3 + (635/4)*x4 <= 170000, 'Budget Constraint' problem += 5*x1 + 8*x2 + 5*x3 + (5/4)*x4 <= 82, 'Space Constraint' problem += x1 + x2 >= 0.3*(x1 + x2 + x3 + x4), 'Promotional Constraint' problem += x3 >= 2*x4, 'Sales Constraint'

# Solve the problem and generate sensitivity report problem.solve(pulp.PULP_CBC_CMD(msg=0)) print("Status: ", pulp.LpStatus[problem.status]) print("Objective Function Value: $", round(pulp.value(problem.objective), 2)) for variable in problem.variables(): print(variable.name, "=", variable.varValue) for name, constraint in problem.constraints.items(): print(name, "Slack Value =", round(constraint.slack, 2)) print(name, "Shadow Price =", round(constraint.pi, 2))

for name, constraint in problem.constraints.items(): print(name, "Slack Value =", round(constraint.slack, 2)) print(name, "Shadow Price =", round(constraint.pi, 2)) ]

im stuck with this : "generate a sensitivity report". can you please generate a sensitivity report?

thanks