To find the new optimal objective value when changing multiple resources simultaneously, first apply the 100% Rule by checking if the sum of each constraint's change relative to its maximum allowable increase or decrease is less than or equal to one. If this condition holds, the current optimal basis remains valid, and you can calculate the new objective value by adding the product of each resource change and its corresponding shadow price to the current objective value. If the sum exceeds 100%, the optimal basis changes, requiring the linear program to be re-optimized to find the new value.

When two resource constraints are modified simultaneously, calculate the effect of each RHS change using its shadow price, then add both effects to the original optimal objective value. In words, new objective value equals original objective value plus the first shadow price multiplied by its RHS change plus the second shadow price multiplied by its RHS change. This can be used when the combined changes satisfy the 100% Rule; otherwise, the current shadow prices may no longer be valid and the problem should be re-solved.

You can use the shadow prices to estimate the change in the objective value. Multiply each change in the resource constraint by its shadow price, then add the results to the original optimal objective value, as long as the changes stay within the allowable ranges.