Question

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

11

unit of nutrient A and

22

units of nutrient​ B; the chicken flavored biscuits contain

11

unit of nutrient A and

44

units of nutrient B. According to federal​ requirements, there must be at least

4040

units of nutrient A and

6060

units of nutrient B in a package of the new mix. In​ addition, the company has decided that there can be no more than

1616

liver flavored biscuits in a package. It costs

11​¢

to make 1 liver flavored biscuit and

22​¢

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:

Xequals=number

of liver flavored biscuit in a package

Yequals=number

of chicken flavored biscuit in a package

​a) Objective​ Function:

Minimize

Z.

Min Z​ (in ​cents)equals=

11Xplus+22Y

Subject​ to:

11Xplus+11Y

greater than or equals≥ 4040

​(Upper C 1C1​)

22Xplus+44Y

greater than or equals≥ 6060

​(Upper C 2C2​)

		11Xplus+00Y	less than or equals≤1616	​(Upper C 3C3​)
		​X,Ygreater than or equals≥0

​b) On the graph on​ right, constraints

Upper C 1C1​,

Upper C 2C2

and

Upper C 3C3

have been drawn using the line drawing tool.  

Using the point drawing

tool​,

plot the corner points for the feasible area.

Answer 1

LP model is following:

Min 1X+2Y

s.t.

1X+1Y >= 40

2X+4Y >= 60

1X+0Y <= 16

X, Y >= 0

Graphical representation is follows:

Feasible region is the dark red region bounded on one side by corner points (0,40), and (16,24). The feasible region is unbounded extending upto infinity along the Y-axis

Value of objective function is the minimum at point (16,24)

Therefore, optimal solution is:

X = 16

Y = 24

Objective function value = 64