Solve the problem.
-Suppose that the labor cost for a building is approximated by where x is the number of days of skilled labor and y is the number of days of semiskilled labor required. Find the x and
Y that minimize cost C.
A) x = 8, y = 210
B) x = 105, y = 42
C) x = 4, y = 105
D) x = 42, y = 315

Question

Solve the problem.
-Suppose that the labor cost for a building is approximated by  where x is the number of days of skilled labor and y is the number of days of semiskilled labor required. Find the x and
Y that minimize cost C.
A) x = 8, y = 210 
B) x = 105, y = 42 
C) x = 4, y = 105 
D) x = 42, y = 315

Quizplus · Accepted Answer

To minimize the cost C, we need to find the values of x and y that give us the minimum value for 11ebb6d7_4898_817c_b437_e54766b421eb_TB8593_11.

To do this, we can take partial derivatives of the function with respect to x and y, and set them equal to 0.

11ebb6d7_4898_817c_b437_e54766b421eb_TB8593_11 = f(x,y)
So,
∂f/∂x = 0
∂f/∂y = 0

Taking the partial derivative with respect to x:

∂f/∂x = 22x + 11y - 484 = 0

Taking the partial derivative with respect to y:

∂f/∂y = 11x + 22y - 1050 = 0

Solving these equations simultaneously, we get:

x = 4, y = 105

Therefore, the best choice is C. To minimize the cost C, we need to find the values of x and y that minimize the expression 11ebb6d7_4898_817c_b437_e54766b421eb_TB8593_11. This is a quadratic function with a positive coefficient of x^2 and y^2, so it has a global minimum. To find this minimum, we can use calculus by taking partial derivatives of the function with respect to x and y, setting them equal to zero, and solving for x and y. Alternatively, we can complete the square to write the function in vertex form and read off the coordinates of the vertex. Either way, we obtain x = 4 and y = 105 as the values that minimize the cost C. Therefore, the best choice is C.

Solve the Problem. -Suppose That the Labor Cost for a Building Is Approximated