Mercer, Inc., maintains a defined benefit pension plan for its employees. As of December 31, the fair value of the plan assets is less than the accumulated benefit obligation and less than the projected benefit obligation. The PBO exceeds the ABO. In its balance sheet as of December 31, Mercer should report a liability for pension benefits in the amount of the Excess of the ABO over the fair value of the plan assets. Excess of the PBO over the fair value of the plan assets. PBO. ABO.

Step-by-step explanation:

If x represents the number of $1 increases from $10 in the cost of the buffet, then the cost per customer is ...

  c(x) = 10 +x

If n represents the number of customers for a given number of $1 increases (x), then we have ...

  n(x) = 16 -2x

The revenue will be the product of these:

  r(x) = c(x)n(x) = (10 +x)(16 -2x)

  r(x) = -2x^2 -4x +160

Then the desired inequality is ...

  r(x) ≥ 130

  -2x^2 -4x +160 ≥ 130

The solution to this is ...

  -2x^2 -4x +30 ≥ 0 . . . .subtract 130

  x^2 +2x -15 ≤ 0 . . . . . . divide by -2

  (x +5)(x -3) ≤ 0

The factors both have the same sign (hence a positive product) for x < -5 or x > 3. One of them is negative in the interval (-5, 3), so that is the solution to the inequality.

  -5 ≤ x ≤ 3

Noah could charge $12 or $13 and maintain his revenue.

The maximum possible increase that maintains Noah's revenue is $3. This is the upper end of the solution space for the inequality.