wishes to introduce a new brand of dog biscuits composed of chicken and biscuits
ID: 347378 • Letter: W
Question
wishes to introduce a new brand of dog biscuits composed of chicken and biscuits contain 1 unit of nutrient A and 4 units of has decided that there can be no more The liver flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B: the chicken nutrient B nutrient B in a than 10 liver chicken favored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the firm's cost to federal requirements, there must be at least 40 units of nutrient A and 60 units of of the new mix. In addition, the biscuits in a package. It costs 1e to make 1 liver flavored biscuit and 2e to make 1 Develop the L.P. Model for Doug to determine the optimal solution x number of liver flavored biscuit in a package Y number of chicken flavored biscuit in a package Min Z (in cents)-ix 2Y 10 X 1Y2 40 (C1) 2X +4Y 2 60 (C2)Explanation / Answer
Let the no. of liver flavored biscuits be “x” and no. of chicken flavored biscuits be “y”
Objective function = 1x+2y and this has to be minimized.
Constraints:
1. 1x+1y>=40 (with regards to nutrient A)
2. 2x+4y>=60 (with regards to nutrient B)
3. x<=10
4. x,y>=0 and should be integers.
The graph has already been plotted by you. From the graph the intersevtion of points (40,40) with the point x = 10 and the points (0,40) and (10,45) lie in the feasible region.
Interection of points (40,40) with the point x = 10 will give us the point (10,30)
Thus the corner points are (10,30), (0,40) and (10,45)
Objective function with 10,30 = 10+(2*30) = 70
Objective function with (0,40) = 0+(2*40) = 80
Objective function with (10,45) = 10+(2*45) = 100
We can see that the value of the objective function is minimum at (10,30) when the total cost = 70
Thus x = 10 and Y = 30 and the minimized cost = 70. All constraints are satisfied.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.