Part A Please read and review the material presented in the attached MS Power Point (Fish_and_Chips) Download (Fish_and_Chips). This will help you better conceptualize and understand what the solutions of simultaneous equations in two-(2) variables/dimensions tells us...plus, what a Chippy is! =) Part B The solution for part A was obtained by graphically finding the intersection of the two lines. There are other ways to arrive at the same conclusion by the substitution method of using matrices. Please verify the solution presented in part A two-(2) ways: Solve by the elimination or substitution method.

Resource: System of Equations Calculator - SymbolabLinks to an external site. You select or type the work substitution or elimination followed by each equation separated by a comma. Solve by applying the inverse matrix property. Recall if AX = B, then we multiply both sides by the inverse matrix of A or (A-1 )X = (A-1 )B to find the solution X = (A-1 )B. Resource: Matrix Calculator (mathsisfun.com)Links to an external site. https://www.mathsisfun.com/algebra/matrix-calculator.htmlLinks to an external site. W2_Assignment_Image_2.png W2_Assignment_Image_3.png Change the dimensions using the arrows and then select inv(A). Then click to A to replace A with inv(A). W2_Assignment_Image_4.png Now click AB to multiply (A-1 )B and find the solution. Part C Please setup the following maximization problem and then solve it. [That is you want to Maximize the Objective function Subject to the Constraints.] A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 180 and 300. The time requirements and profit per unit for each product are listed below. A

B

C

Machine I

1

2

2

Machine II

2

2

4

Profit

20

30

40

How many units of each product should be manufactured to maximize profit, and what is the maximum profit? As usual, we start by defining our variables: A = number of units of product A manufactured B = number of units of product B manufactured C = number of units of product B manufactured Resource: simplex me - the simple simplex solverLinks to an external site. http://www.simplexme.com/en/Links to an external site. Note: When using the simplex solver the variables are A=x1, B=x2 & C=x3 Please setup the following minimization problem and then solve it. [That is, you want to Minimize the Objective function Subject to the Constraints.] A company is creating a meal replacement bar. They plan to incorporate peanut butter, oats, and dried cranberries as the primary ingredients. The nutritional content of 10 grams of each is listed below, along with the cost, in cents, of each ingredient. Find the amount of each ingredient they should use to minimize the cost of producing a bar containing a minimum of 15g of each ingredient, at least 10g of protein and at most 14g of fat. Peanut Butter, 10g

Oats, 10g

Cranberry, 10 g

Protein (grams)

2.5

1.7

0

Fat (grams)

5

0.7

0.1

Cost (cents)

6

1

2

We start by introducing variables: p = number of 10g servings of peanut butter a = number of 10g servings of oats c = number of 10g servings of cranberries Resource: simplex me - the simple simplex solverLinks to an external site. Note: When using the simplex solver the variables are p=x1, o=x2 & c=x3 ***Helpful Hint - Please visit the "Open Sourse Textbook PDF Resource" below for guidance with setting up the problems in Part C above. =)

Open Source Textbook PDF Resource