How much will it cost to ship the number of blenders that yields the company its

Question

  How much will it cost to ship the number of blenders that yields the company its maximum profit? How much will it cost the company to ship the number of blenders that yields the company a profit of 0?

   Assuming it costs $20 to produce each blender, complete the following chart and calculate the revenue. Fill in the empty rows with data obtained for the number of blenders that yield maximum profit and a profit of zero.

Number of Blenders

Production Cost (dollars)

Shipping Cost (dollars)

Profit (dollars)

Revenue (dollars)

10

200

38

-1314.30

30

60

100

   Do the revenue amounts make sense? If not, what could possibly be a reason? What other factors could be influencing the profit? In 3-5 sentences elaborate on your findings.

Number of Blenders

Production Cost (dollars)

Shipping Cost (dollars)

Profit (dollars)

Revenue (dollars)

10

200

38

-1314.30

30

60

100

y0.01r2 + 3.5x + 4

Explanation / Answer

the profit function is P(x)

Revenue function is R(x)

and the cost function is C(x)

Then P(x) = R(x) - C(x)

here we see that the production cost will be higher if the number of units produced is less. but if you increase the output will also increase and the production cost per unit will decrease. so profit increases.

The present data gives only cost function only.

From this cost function we can find out the maximum value using differentiation

Differentiate the given equation

y= -0.01x2 +3.5x+4

dy/dx = -0.02x +3.5 =0 we set it to zero to find the value of x

so, x= 3.5/-0.02 = 175

now double differentiate it to get

d2y/dx2 = -0.02 The negative value indicates the maximization point. So at x= 175 the function is maximum.

( some data is missing regarding profit function and revenue function here)

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