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 15 liver-flavored biscuits in a package. If it costs 1¢ to make 1 liver-flavored biscuit and 2¢ to make 1 chicken-flavored, what is the optimal product mix for a package of the biscuits to minimize the

Answer 1

To find the optimal product mix, set up a linear programming problem to minimize cost while meeting nutritional requirements and constraints.

Step-by-step explanation:

To find the optimal product mix for the package of dog biscuits, we can set up a linear programming problem. Let's assume the number of liver-flavored biscuits in the package is represented by L and the number of chicken-flavored biscuits is represented by C.

The objective function to minimize the cost would be 0.01L + 0.02C since it costs 1¢ to make 1 liver-flavored biscuit and 2¢ to make 1 chicken-flavored biscuit.

The constraints would be:

• 1L + 1C ≥ 40 (nutrient A requirement)
• 2L + 4C ≥ 60 (nutrient B requirement)
• L ≤ 15 (limit on liver-flavored biscuits)

By solving this linear programming problem, we can find the values of L and C that minimize the cost while meeting the nutritional requirements and constraints.

Answer 2

Answer: opt value = 65

Step-by-step explanation:

This is quite easy to solve.

we will take a step by step process to solving this problem.

attached below are images showing the sheet for the formula used to run the program as well as the output(answer).

Let us begin;

we have from the problem that the variables Given are;

Y which is the number of chicken flavored biscuits in a package

and X represent the number of chicken flavored biscuits in a package7

Taking LLP as follows:

Min Z = 1X + 2Y where Z rep the Objective Minimum Function

subject to

1X + 1Y >= 40

2X + 4Y >= 60

1X + 0Y <= 15

X, Y >= 0

(i). attached is the excel sheet housing the formula

(ii). attached is the sheet generating the values

(iii). attached is the Excel solver

(iv). attached is final sheet showing the results

We have that the No of Liver Flavored biscuits and No of Chicken Flavored biscuits is 15 & 25

From the attached result, we have that the optimum solution value is 65