Question

A pet food manufacturer produces two types of food: Regular and Premium. A 20kg bag of regular food requires 3 hours to prepare and 5 hours to cook. A 20kg bag of premium food requires 3 hours to prepare and 6 hours to cook. The materials used to prepare the food are available 9 hours per day, and the oven used to cook the food is available 16 hours per day. The profit on a 20kg bag of regular food is $42 and on a 20kg bag of premium food is $34.

(a) What can the manager ask for directly?

		Number of bags of premium pet food made per day
		Number of bags of regular pet food made per day
		Profit in a day
		Preparation time in a day
		Oven time in a day

The manager wants xbags of regular food and ybags of premium pet food to be made in a day.

(b) Enter the constraint imposed by available preparation time. It will be an inequality involvingxand y, you can enter less than or equal to, and greater than or equal to, as <= and >= respectively.

(c) Enter the constraint imposed by available time in the oven.


(d) Enter the total profit as a function of xand y.

(e) Plot the inequalities on a graph. Enter the coordinates of the corners of the feasible region (the feasible basic solutions). Enter them in increasing order of their x-coordinate. For example, if one feasible basic solution is x=1,y=2; another is x=5,y=0and a third is x=2,y=3, you would enter (1,2), (2,3), (5,0) If two feasible basic solutions have the same x-value, enter them in increasing order of y-value. Enter them exactly, with fractions if necessary (they will just produce smaller bags)


(f) Calculate the daily profit of each of these feasible basic solutions. What is the greatest possible profit in a day?

Answer 1

a) The manager can ask for directly

Number of bags of premium pet food made per day

Number of bags of regular pet food made per day

Profit in a day

b) The preparation time and cooking time for each type can be written as below;

	Regular(x)	Premium (y)	Availibility
Preparation	3	3	9
Cooking	5	6	16

The preparation time constraint is

c) The cooking time constraint is

d) The profit on a 20kg bag of regular food is $42 and on a 20kg bag of premium food is $34.

the objective function can be written as

e) The feasible region is as shown below, region OABC

The feasible solutions are

(0,2.6) , (2,1) and (3,0)

f)

Max profit in a day is $126 at (3,0) i.e. to produce 3 bags of regular and n bags of premium food