A manufacturer’s costs per unit of production is based on the following function. In the function, x is the number of units produced in a day and f(x)

Question

is the cost in dollars per unit of production.

f⎛⎝⎜x⎞⎠⎟=⎧⎩⎨⎪⎪1.50,1.00,0.85,0<x<10,00010,000≤x<30,00030,000≤x≤45,000


Select the paragraph that correctly interprets the function.

(1 point)
Responses

The cost per unit of production is based on the equations of three line segments with non-negative slopes. The equation of the line segment for 0 units to 10,000 units is y=1.5010,000x
. The equation of the line segment for 10,000 units to 30,000 units is y−1.50=−0.5020,000(x−10,000)
. The equation of the line segment for 30,000 units to 45,000 units is y−1.00=−0.1515,000(x−30,000)
.

The cost per unit of production is based on the equations of three line segments with non-negative slopes. The equation of the line segment for 0 units to 10,000 units is y = 1 . 50 10 , 000 x . The equation of the line segment for 10,000 units to 30,000 units is y - 1 . 50 = - 0 . 50 20 , 000 ( x - 10 , 000 ) . The equation of the line segment for 30,000 units to 45,000 units is y - 1 . 00 = - 0 . 15 15 , 000 ( x - 30 , 000 ) .

The cost per unit of production is based on the equations of three line segments with non-negative slopes. The equation of the line segment for 0 units to 10,000 units is y=1.5010,000x
. The equation of the line segment for 10,000 units to 30,000 units is y−1.50=0.5020,000(x−10,000)
. The equation of the line segment for 30,000 units to 45,000 units is y−1.00=0.1515,000(x−30,000)
.

The cost per unit of production is based on the equations of three line segments with non-negative slopes. The equation of the line segment for 0 units to 10,000 units is y = 1 . 50 10 , 000 x . The equation of the line segment for 10,000 units to 30,000 units is y - 1 . 50 = 0 . 50 20 , 000 ( x - 10 , 000 ) . The equation of the line segment for 30,000 units to 45,000 units is y - 1 . 00 = 0 . 15 15 , 000 ( x - 30 , 000 ) .

There are three different costs per unit of production that depend on the number of units produced. The cost per unit of production increases for larger number of units produced. The manufacturer produces no more than 45,000 per day.

There are three different costs per unit of production that depend on the number of units produced. The cost per unit of production increases for larger number of units produced. The manufacturer produces no more than 45,000 per day.

There are three different costs per unit of production that depend on the number of units produced. The cost per unit of production decreases for larger number of units produced. The manufacturer produces no more than 45,000 per day.

Answer 1

The correct interpretation of the function is:

There are three different costs per unit of production that depend on the number of units produced. The cost per unit of production decreases for larger number of units produced. The manufacturer produces no more than 45,000 per day.

This interpretation accurately reflects the piecewise nature of the cost function provided, where the cost per unit decreases as production increases from 1.50 to 0.85 as the number of units produced goes from 0 to 45,000.