Question

In deciding whether or not to set up a new manufacturing plant, analysts for a popcorn company have decided that a linear function is a reasonable estimation for the total cost C(x) in dollars to produce x bags of microwave popcorn. They estimate the cost to produce 10,000 bags as $5290 and the cost to produce 15,000 bags as $7570 Find the marginal cost of the bags of microwave popcorn to be produced in this plant.

Answer 1

2 coordinates ( 10000, 5290) and ( 15000, 7570)

X1 = 10000

X2 = 15000

Y1 = 5290

Y2 = 7570

from above 2 coordinates,

slope(m) = ( Y2-Y1) / (X2-X1)

= (7570-5290) / (15000-10000)

= 0.456

From the above,

Y= mx+b

Y= 0.456x+b

substitute (10000, 5290) above to find b

5290= 0.456(10000)+b

5290=4560+b

b= 730

Now, Y= 0.456x+730

so, cost C(x) = 0.456x+730

now, marginal cost or derivative of cost

C(x) = d/dx(0.456x+730)

so, c(x) = $ 0.456 per unit