a blending problem

a-blending-problem.lisp

;;;; A Blending Problem

;;; See https://coin-or.github.io/pulp/CaseStudies/a_blending_problem.html

(defvar *blending-ingredients*
  '((chicken :cost 0.013 :protein 0.100 :fat 0.080 :fibre 0.001 :salt 0.002)
    (beef    :cost 0.008 :protein 0.200 :fat 0.100 :fibre 0.005 :salt 0.005)
    (mutton  :cost 0.010 :protein 0.150 :fat 0.110 :fibre 0.003 :salt 0.007)
    (rice    :cost 0.002 :protein 0.000 :fat 0.010 :fibre 0.100 :salt 0.002)
    (wheat   :cost 0.005 :protein 0.040 :fat 0.010 :fibre 0.150 :salt 0.008)
    (gel     :cost 0.001 :protein 0.000 :fat 0.000 :fibre 0.000 :salt 0.000)))

(defun a-blending-problem (&optional (ing-list *blending-ingredients*))
  (with-lp (problem "A Blending Problem" :minimize)
    (flet ((col (indicator) (mapcar (lambda (ing) (getf (cdr ing) indicator)) ing-list)))
      (let ((vars (mapcar (lambda (ing) (var (string-capitalize (car ing)) :continuous 0)) ing-list)))
        (set-objective (dot (col :cost) vars))
        (add-constraint (= vars 100) "Pcts Sum")
        (add-constraint (>= (dot (col :protein) vars) 8) "Protein Req")
        (add-constraint (>= (dot (col :fat) vars) 6) "Fat Req")
        (add-constraint (<= (dot (col :fibre) vars) 2) "Fibre Req")
        (add-constraint (<= (dot (col :salt) vars) 0.4) "Salt Req")
        (solve)))))