Suppose the marginal cost of producing x units of a product is given by: MC=30 Square root (x+4)And the marginal revenue is given by: MR = 900 And the fixed costs are $1000.What is the profit (or loss) for the production and sale of 5 units of this product ?How many units are needed to be sold to make the maximum profit?

Given, Marginal cost is MC=30x+4 where x is units of product. Marginal Revenue is MR=900 Fixed cost = $1000 Formula for the profit is Profit=Revenue-CostRevenue for for the production and sale of 5 units = $900×5=$4500 MC for 1st unit = 301+4=305 MC for 2nd unit = 302+4=306 MC for 3rd unit = 303+4=307 MC for 4th unit = 304+4=308 MC for 5th unit = 305+4=309=303=90 Total MC = 305+306+307+308+90=305+6+7+8+3=$395 Cost=Total MC+Fixed Cost=$395+$1000=$1395 So, Profit=$4500-$1395Profit=$3105we know that, Marginal Profit=Merginal Revenue-Marginal CostMP=900-30x+4Profit is maximum when Margina Profit=0So,MP=0900-30x+4=030x+4=900x+4=90030x+4=30Squaring on both the sides,x+4=302x+4=900x=900-4x=896 unitsTherefore, The profit for the production and sale of 5 units of the product is $3105. 896 units are needed to be sold to make the maximum profit.

Answered: Suppose the marginal cost of producing…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Suppose the marginal cost of producing x units of a product is given by: MC=30 Square root (x+4)

And the marginal revenue is given by: MR = 900 And the fixed costs are $1000.

What is the profit (or loss) for the production and sale of 5 units of this product ?

How many units are needed to be sold to make the maximum profit?

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