Question

I dont know how they got the numbers. I tried different methods and still didnt get the right answer.
Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken and liver flavored biscuits that meet certain nutritional requirements. The liver flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B; the chicken flavored biscuits contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 10 liver flavored biscuits in a package. It costs 1¢ to make 1 liver flavored biscuit and 2¢ to make 1 chicken flavored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the firm's cost. The L.P. Model for Doug to determine the optimal solution is: Variables: X= number of liver flavored biscuit in a package Y = number of chicken flavored biscuit in a package a) Objective Function: Minimize Z. Min Z (in cents) = 1X + 2 Y Subject to: 1X + 1Y 2 40 (C1) 2X +4Y 2 60 (C2) 1X+ OY 510 (C3) X,Y 20

Answer 1

MIN Z = x+27 SE x + Y >40 2x + 4V > 60 x, y, o x+y=40 xol 401 2x + 4y =60 Tol30 Y 1510 x 1010 X=10 X+1340 2x2447,60 o s co 15 20 25 30 35 40 45 50 55

It is an unbounded graph. corner points objective function value ixo + 2x 40 = 80 A (0,40) B (1930) 1810 + 2x30 -20) minimum vale of objective functon is Z=60, at point (10,3o) Hence optimal solution is x = 10 V = 30 objedive Vake Total logd) = 70