Constraints and Objective Functions

Find the values of x and y that maximize the objective function z= 30x + 40y.

• (0, 6)

• (3, 11)

• (6, 0)

• (0, 0)

Find the values of x and y that minimize the objective function z = 4x + 2y.

• (0, 5)

• (0, 15)

• (5, 0)

• none of the above

In linear programming the factors that limit how a quantity is maximized or minimized are called​ what?

• constraints

• objective functions

• matrices

• feasible region

If the feasible region is as shown, which critical point will

max 5x + 2y

• (1,3)

• (0,4)

• (2.5, 0)

• (11, 3)

Tags

A2.ACE.3

For the feasible region shown any point in the green shaded area would satisfy the constraints. Only one point would optimize the objective function.

• True

• False

Tags

A2.ACE.3

A furniture company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labour hours in the painting department. Each table takes 4 hours of carpentry and 2 hours of painting. Each chair requires 3 hours of carpentry and 1 hour of painting. During the current production period, 240 hours of carpentry time are available and 100 hours in painting is available. Each table sold yields a profit of $70.00; each chair produced is sold for a $50.00 profit. Find the best combination of tables and chairs to manufacture in order to reach the maximum profit. What is the objective function?

• min 70x + 50y

• max 70x + 50y

• min 70x - 50y

• max 70x - 50y

Tags

A2.ACE.3

A furniture company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labour hours in the painting department. Each table takes 4 hours of carpentry and 2 hours of painting. Each chair requires 3 hours of carpentry and 1 hour of painting. During the current production period, 240 hours of carpentry time are available and 100 hours in painting is available. Each table sold yields a profit of $70.00; each chair produced is sold for a $50.00 profit. Find the best combination of tables and chairs to manufacture in order to reach the maximum profit. What is the optimal point and the resulting objective function value?

• (0,80) and $400

• (30, 40) and $410

• (50,0) and $350

Tags

A2.ACE.3

​ ​ functions are mathematical expressions that are ​ (a)   by choosing the critical point that ​ (b)   or ​ (c)   the function.

• Objective

• optimized

• maximizes

• minimizes

Tags

A2.ACE.3