C Challenge

23. A vertex of a feasible region does not always have whole-number coordinates. Sometimes you may need to round coordinates to find the solution. Using the objective function and the constraints below, find the whole-number values of x and y that minimize C. Then find C for those values of x and y.

    C = 6 x + 9 y { x + 2 y ≥ 50 2 x + y ≥ 60 x ≥ 0 , y ≥ 0 c equals 6 x plus 9 y . left brace . table with 3 rows and 1 column , row1 column 1 , x plus 2 y greater than or equal to 50 , row2 column 1 , 2 x plus y greater than or equal to 60 , row3 column 1 , x greater than or equal to 0 comma y greater than or equal to 0 , end table

24. Reasoning Sometimes two corners of a graph both yield the maximum profit. In this case, many other points may also yield the maximum profit. Evaluate the profit formula P = x + 2y for the graph shown. Find four points that yield the maximum profit.

    

Standardized Test Prep

SAT/ACT

25. Solve the equation 1 2 ( a + b ) = c 1 half , open eh plus b close equals c  for b.
    1. b = 1 2 c − a b equals , 1 half , c minus eh
    2. b = 2 a − c b equals 2 eh minus c
    3. b = 2 c − a b equals 2 c minus eh
    4. b = 2ca
26. Which is the graph of y ≤ | x − 3 | ? y less than or equal to vertical line x minus 3 vertical line question mark
    6. 
    7. 
    8. 
    9. 

Short Response

27. What are the vertices of the feasible region bounded by the constraints below?

    { x + y ≤ 3 2 x + y ≤ 4 x ≥ 0 , y ≥ 0 left brace . table with 3 rows and 1 column , row1 column 1 , x plus y less than or equal to 3 , row2 column 1 , 2 x plus y less than or equal to 4 , row3 column 1 , x greater than or equal to 0 comma y greater than or equal to 0 , end table

Mixed Review

See Lesson 3-3.

Solve each system of inequalities by graphing.

28. { y < − 2 x + 8 3 y ≥ 4 x − 6 left brace . table with 2 rows and 1 column , row1 column 1 , y less than negative 2 x plus 8 , row2 column 1 , 3 y greater than or equal to 4 x minus 6 , end table
29. { x − 2 y ≥ 11 5 x + 4 y < 27 left brace . table with 2 rows and 1 column , row1 column 1 , x minus 2 y greater than or equal to 11 , row2 column 1 , 5 x plus 4 y less than 27 , end table
30. { 2 x + 6 y > 12 3 x + 9 y ≤ 27 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus 6 y greater than 12 , row2 column 1 , 3 x plus 9 y less than or equal to 27 , end table

See Lesson 1-3.

Evaluate each expression for a = 3 and b = − 5 . b equals negative 5 .

31. 2a + b
32. − 4 + 2 a b negative 4 plus 2 eh b
33. 3 ( a − b ) 3 open eh minus b close
34. b ( 2 b − a ) b open 2 b minus eh close

Get Ready! To prepare for Lesson 3-5, do Exercises 35–37.

See Lesson 2-4.

Find the x- and y-intercepts of the graph of each linear equation.

35. y = 2x + 6
36. 2x + 9y = 36
37. y = x − 1 y equals x minus 1

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