Linear programming (linprog) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple linear programming problem

What is the output of the following code that solves a linear programming problem?

SciPy

from scipy.optimize import linprog

c = [-1, -2]
A = [[2, 1], [1, 1]]
b = [20, 16]

result = linprog(c, A_ub=A, b_ub=b, method='highs')
print(result.x.round(2))

A [5. 5.]

B [10. 0.]

C [8. 8.]

D [0. 16.]

💡 Hint

Think about maximizing the objective by minimizing the negative coefficients under the constraints.

The linear program minimizes -x - 2y subject to 2x + y ≤ 20 and x + y ≤ 16. The optimal solution is x=0, y=16.

❓ data_output

intermediate

Number of iterations in linprog solution

How many iterations does the solver take to solve this linear programming problem?

SciPy

from scipy.optimize import linprog

c = [3, 1]
A = [[1, 2], [4, 0]]
b = [8, 16]

result = linprog(c, A_ub=A, b_ub=b, method='highs')
print(result.nit)

A 0

B 2

C 3

D 1

💡 Hint

Check the solver's iteration count attribute after solving.

The 'highs' method often solves small problems in zero iterations because it uses advanced presolve techniques.

🔧 Debug

advanced

Identify the error in linear programming code

What error will this code raise when executed?

SciPy

from scipy.optimize import linprog

c = [1, 2]
A = [[-1, 1], [1, -2]]
b = [1, 2]

result = linprog(c, A_eq=A, b_eq=b, method='highs')
print(result.success)

A No error, prints False

B ValueError: A_eq and b_eq dimensions mismatch

C LinAlgError: Singular matrix

D TypeError: unsupported operand type(s)

💡 Hint

Check if the dimensions of A_eq and b_eq match and if the problem is feasible.

The dimensions of A_eq (2x2) and b_eq (length 2) match, but the problem is infeasible because the equality constraints require negative values for the variables (x=-4, y=-3), which violate the default bounds x >= 0, y >= 0, so no error occurs and success is False.

🚀 Application

advanced

Interpreting linprog results for resource allocation

A factory produces two products with profits $5 and $3 per unit. It has 40 hours of labor and 30 units of raw material. Labor and material requirements per product are:

• Product 1: 2 hours labor, 1 unit material
• Product 2: 1 hour labor, 2 units material

Using linprog, what is the maximum profit?

SciPy

from scipy.optimize import linprog

c = [-5, -3]
A = [[2, 1], [1, 2]]
b = [40, 30]

result = linprog(c, A_ub=A, b_ub=b, method='highs')
print(round(-result.fun, 2))

A 80.0

B 75.0

C 103.33

D 105.0

💡 Hint

Remember to negate the objective function value to get maximum profit.

The optimal production mix yields a maximum profit of $103.33 by solving the constraints and maximizing profit.

🧠 Conceptual

expert

Understanding linprog infeasibility output

What does the linprog result indicate if result.success is False and result.status is 2?

A The problem is unbounded; objective can decrease indefinitely.

B The problem is infeasible; no solution satisfies all constraints.

C The solver encountered a numerical error during optimization.

D The problem has multiple optimal solutions.

💡 Hint

Check the meaning of status codes in linprog documentation.

Status code 2 means the problem is infeasible, so no solution meets all constraints.