diff --git a/src/Utilities/results.jl b/src/Utilities/results.jl
index 981135ab02..151debdce4 100644
--- a/src/Utilities/results.jl
+++ b/src/Utilities/results.jl
@@ -108,6 +108,29 @@ function _dual_objective_value(
     return set_dot(constant, dual, set)
 end
 
+function _dual_objective_value(
+    model::MOI.ModelLike,
+    ci::MOI.ConstraintIndex{<:MOI.AbstractVectorFunction,<:MOI.HyperRectangle},
+    ::Type{T},
+    result_index::Integer,
+) where {T}
+    func_constant =
+        MOI.constant(MOI.get(model, MOI.ConstraintFunction(), ci), T)
+    set = MOI.get(model, MOI.ConstraintSet(), ci)
+    dual = MOI.get(model, MOI.ConstraintDual(result_index), ci)
+    constant = map(eachindex(func_constant)) do i
+        return func_constant[i] - if dual[i] < zero(dual[i])
+            # The dual is negative so it is in the dual of the MOI.LessThan cone
+            # hence the upper bound of the Interval set is tight
+            set.upper[i]
+        else
+            # the lower bound is tight
+            set.lower[i]
+        end
+    end
+    return set_dot(constant, dual, set)
+end
+
 function _dual_objective_value(
     model::MOI.ModelLike,
     ::Type{F},
@@ -116,23 +139,18 @@ function _dual_objective_value(
     result_index::Integer,
 ) where {T,F<:MOI.AbstractFunction,S<:MOI.AbstractSet}
     value = zero(T)
+    if F == variable_function_type(S) && !_has_constant(S)
+        return value # Shortcut
+    end
     for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
         value += _dual_objective_value(model, ci, T, result_index)
     end
     return value
 end
 
-function _dual_objective_value(
-    ::MOI.ModelLike,
-    ::Type{MOI.VectorOfVariables},
-    ::Type{<:MOI.AbstractVectorSet},
-    ::Type{T},
-    ::Integer,
-) where {T}
-    # No constant in the function nor set so no contribution to the dual
-    # objective value.
-    return zero(T)
-end
+_has_constant(::Type{<:MOI.AbstractScalarSet}) = true
+_has_constant(::Type{<:MOI.AbstractVectorSet}) = false
+_has_constant(::Type{<:MOI.HyperRectangle}) = true
 
 """
     get_fallback(
diff --git a/test/Utilities/results.jl b/test/Utilities/results.jl
new file mode 100644
index 0000000000..5286604f7d
--- /dev/null
+++ b/test/Utilities/results.jl
@@ -0,0 +1,56 @@
+# Copyright (c) 2017: Miles Lubin and contributors
+# Copyright (c) 2017: Google Inc.
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+module TestResults
+
+using Test
+
+import MathOptInterface as MOI
+
+function runtests()
+    for name in names(@__MODULE__; all = true)
+        if startswith("$(name)", "test_")
+            @testset "$(name)" begin
+                getfield(@__MODULE__, name)()
+            end
+        end
+    end
+    return
+end
+
+test_hyperrectangle_Int() = _test_hyperrectangle(Int)
+
+test_hyperrectangle_Float64() = _test_hyperrectangle(Float64)
+
+function _test_hyperrectangle(T)
+    model = MOI.Utilities.MockOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{T}()),
+        T,
+    )
+    x = MOI.add_variables(model, 2)
+    c1 = MOI.add_constraint(
+        model,
+        MOI.VectorOfVariables(x),
+        MOI.HyperRectangle(T[3, -7], T[5, -2]),
+    )
+    c2 = MOI.add_constraint(
+        model,
+        MOI.Utilities.vectorize(x .+ T[11, 13]),
+        MOI.HyperRectangle(T[-T(6), -T(4)], [T(3), T(2)]),
+    )
+    MOI.set(model, MOI.ConstraintDual(), c1, T[4, -3])
+    MOI.set(model, MOI.ConstraintDual(), c2, T[-2, 5])
+    @test -53 == @inferred MOI.Utilities.get_fallback(
+        model,
+        MOI.DualObjectiveValue(),
+        T,
+    )
+    return
+end
+
+end  # module TestResults
+
+TestResults.runtests()