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

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.

Number of liver flavored biscuits in a package​ =

​(round your response to two decimal​ places).

Answer 1

Let X = number of liver-flavored biscuits

Y=number of chicken-flavored biscuits

Objective: Minimize cost------C=$0.01X+0.02Y

Constraints: X+Y>=40

2X + 4Y >= 60

X<=10

X,Y>=0.

Draw the graph of x+y=40 ..... (i)
We get intersection of (i) with the coordinate axes at points (0,40) and (40,0)
Draw the graph of 2x+4y=60 ..... (ii) and

We get the intersection of (ii) with the coordinate axes at points (0,15) and (30,0)
Draw the graph of x= 10 ...... (iii) so our intersection is (10,0)

My corner points are (0,40) & (10,30)

Minimization of z= 0.01x +0.02y= 0.01*10+0.02*30=70 cents

Number of liver flavored biscuit in a package=10