project3.sagews

load('/home/user/lenprogram.sage')

# P = Protien
# C = Carbohydrates
# F = Fat
# Fr = Fruit, servings
# M = Meat, servings
# V = Vegetable, servings

# FrC = Cost per serving of fruit, dollars
# MC = Cost per serving of meat, dollars
# VC = Cost per serving of vegetable, dollars

# FrP = Protein in 1 serving of fruit, grams
# FrC = Carbs in 1 serving of fruit, grams
# FrF = Fat in 1 serving of fruit, grams

# MP = protein in 1 serving of meat, grams
# MC = carbs in 1 serving of meat, grams
# MF = fat in 1 serving of meat, grams

# VP = protein in 1 serving of vegetable, grams
# VC = carbs in 1 serving of vegetable, grams
# VF = fat in 1 serving of vegetable, grams

# Constraints

# FrP + MP + VP >= 56
# FrC + MC + VC >= 130
# FrF + MF + VF >= 65
# FrCa + Mca + Vca >= 100

# Objective Minimize the cost

applesauce = [0,27,0,0] # item = [protein, carbs, fat, calcium]
applesauce_p = 3.5
applesauce_servings = 11
applesauce_c = applesauce_p/applesauce_servings
applesauce_c_serving = [applesauce_c / x for x in applesauce] # applesauce_c/x
applesauce_c_serving

[+infinity, 0.0117845117845118, +infinity, +infinity]

spinach = [2, 3, 0, 8]
spinach_p = 1.54
spinach_servings = 3.5
spinach_c = spinach_p / spinach_servings
spinach_c_serving = [spinach_c / x for x in spinach] # spinach_c/x
spinach_c_serving

[0.220000000000000, 0.146666666666667, +infinity, 0.0550000000000000]

groundbeef = [21, 0, 17, 0]
groundbeef_p = 3.86
groundbeef_servings = 4
groundbeef_c = groundbeef_p / groundbeef_servings
groundbeef_c_serving = [groundbeef_c / x for x in groundbeef] #groundbeef_c/x
groundbeef_c_serving

[0.0459523809523810, +infinity, 0.0567647058823529, +infinity]

protein = [applesauce[0], spinach[0], groundbeef[0]] # I guess this are the M the matrix of coefficients of each row 
carbs = [applesauce[1], spinach[1], groundbeef[1]]
fat = [applesauce[2], spinach[2], groundbeef[2]]

var = ['fruit (servings)', 'veg (servings)', 'meat (servings)']
#con = ['protein', 'carbs', 'fat']
#ob = [applesauce, spinach, groundbeef]
#M= [[1,1,1],[1,1,1],[1,1,1]]
#inq = [-1,-1,-1]
#bnd = [56,130,65]
#lp(var,con,ob,M,inq,bnd, mx = False)
constraint = ['protein', 'carbs', 'fat']
objective = [applesauce_c, spinach_c, groundbeef_c]
coeffs = [protein,carbs,fat]
ineqality = [-1, -1, -1]
bound = [56, 130, 65]
lp( var, constraint, objective, coeffs, ineqality, bound, mx = False)

GLPK 4.60 - SENSITIVITY ANALYSIS REPORT Page 1 Problem: Objective: 5.221692414 (MINimum) No. Row name St Activity Slack Lower bound Activity Obj coef Obj value at Limiting Marginal Upper bound range range break point variable ------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ 1 protein BS 80.29412 -24.29412 56.00000 +Inf -.04595 1.53199 fat . +Inf 80.29412 +Inf +Inf 2 carbs NL 130.00000 . 130.00000 . -.01178 3.68971 fruit (servings) .01178 +Inf +Inf +Inf +Inf 3 fat NL 65.00000 . 65.00000 45.33333 -.05676 4.10532 protein .05676 +Inf +Inf +Inf +Inf GLPK 4.60 - SENSITIVITY ANALYSIS REPORT Page 2 Problem: Objective: 5.221692414 (MINimum) No. Column name St Activity Obj coef Lower bound Activity Obj coef Obj value at Limiting Marginal Upper bound range range break point variable ------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ 1 fruit (servings) BS 4.81481 .31818 . +Inf . 3.68971 carbs . +Inf -Inf 3.96000 22.75637 veg (servings) 2 veg (servings) NL . .44000 . -12.14706 .03535 .30643 protein .40465 +Inf 43.33333 +Inf 22.75637 fruit (servings) 3 meat (servings) BS 3.82353 .96500 . +Inf . 1.53199 fat . +Inf 3.82353 +Inf +Inf End of report