“…Parameter c is specified on the basis of farm management data (see Nakashima 29 for the procedure), and once specified, it is denoted as ĉ. Given that the optimum dual variables associated with resource constraints coincide both in the QP model (1)- (3) and the LP model (4)- (7) The problem is that, without additional information, equation (8) does not have a unique solution in d and Q because there are fewer equations than unknowns to be calibrated (i.e., n < n + 0.5n (n + 1)), which is why this type of calibration is referred to as an ill-posed problem 32 . To solve the ill-posed problem, the following assumption has frequently been imposed: Assumption 1: Matrix Q is diagonal; that is, q ij = 0 if i ≠ j, where q ij (i = 1,2,…, n; j = 1,2,…, n) are the elements of Q. Assumptions 2.1 and 2.2 reduce the number of equations to match the number of parameters to be calibrated; therefore, respective unique solutions can be derived from equation (9) as…”