What is the corresponding system of equations? Restate the problem in terms of equations by adding slack variables or subtracting surplus variables as necessary. Then write the initial simplex tableau. X1 + X2 + X3 + s, = 69 $2 = 48 + S3 = 60 x1 20, x2 2 0, x3 2 0, s, 2 0, s2 2 0, S3 20 Maximize z=2x, +3x2 - 4x3 X1 + X2 + X3 subject to X1 +x2 +X3 S69 X1 +x2 X1 + X2 +X3 248 X1 +X2 X1 20, x2 2 0, X3 20 <60 Write the initial simplex tableau, omitting the z column. Fill in the missing values. X1 X2 X3 S1 $2 S3 1 1 1 0 69 1 1 1 이 48 1 1 60 4 이 ....

The linear system is not in echelon form. Correct Letter(s): 6x1 Begin by choosing which of the following statements are correct. If there is more than one reason why the system is not in echelon form, type the letters as a comma separated list. Now write the system in echelon form. Equation 1: Equation 2: Equation 3: 3x3 = -6 3x3 X2 + 7x2 + 3x3 A. The system is not in echelon form because a variable is the leading variable of two or more equations. - B. The system is not in echelon form because the system is not organized in a descending "stair step" pattern so that the index of the leading variables increases from the top to bottom. stem is not in echelon form because not every equation has a leading variable. (x1, x2, x3): = = 0 12 Finally, solve the system. Use x1, x2, and x3 to enter the variables x₁, x2, and x3. If necessary, use s1, s2, etc. to enter the free variables $1, 82, etc. -(000)

Ahmed wants to make an award made out of different metals. A portion of the trophy is 80% silver and the rest is 44% copper. Ahmed needs 50.0 grams of 72% mixed metals. How much of each allows should he use? Define your variables, create the systems of linear equations. Complete the problem with a word statement. Round to the nearest tenth decimal (one decimal place).

4. 9 An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices. If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation. Peyton thinks that small sundaes cost $2.75 and large sundaes cost $6.75. Is Peyton correct? Justify your answer. Using your equations, determine algebraically the cost of one small sundae and the cost of one large sundae.