0.67/1 points1 Previous Answers HarMathAp11 12.4 009 Cost, revenue, and profit a

Question

0.67/1 points1 Previous Answers HarMathAp11 12.4 009 Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal revenue for a product is MRE 1800 and the marginal cost is MC = 90V 4, with a fixed cost of $500. (a) Find the profit or loss from the production and sale of 5 units. There is aprofit '/ of b) How many units will result in a maximum profit? 396 units Need Help? Emana Your work in queston(s) 3 will also be submitted or saved Submit Assignment Save Assignment Progress Practice Another Version

Explanation / Answer

Marginal Revenue=d(Revenue)/d(quantity) where quantity is given by x

So, MR=dR/dx

=>Total Revenue=1800x+c

As at x=0, totral revenue =0

So, Total Revenue=1800x

Marginal Cost=d(Cost)/d(quantity)

MC=dCost/dx

So, Total Cost=60(x+4)^3/2+c

Fixed cost would occur regardless of any production..So, As given at x=0, cost is 500

hence, c+480=500

=>c=20

Total cost=60(x+4)^3/2+20

The profit function=Total Revenue-Total Cost=1800x-60(x+4)^3/2-20

At x=5, profit=1800*5-60*9^3/2-20=7360 profit

Maximum Profit would occur when Marginal Revenue=Marginal Cost

So, 1800=90*(x+4)^0.5

=>x=396 units

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