Question

Problem 1: A company produces an item at a per-unit cost of $1000 and a fixed cost of $50,000. The selling price is a linear function of number of items demanded as follows: p = 15,000 - 200x, x5 80 A. Find the per-unit selling price when the demand is 30. B. Find the revenue function and find the revenue when the demand is 30. C. Find the cost function and find the cost when the demand is 30. D. Find the profit function and find the profit when the demand is 30. E. Plot the profit versus number of units produced. F. Determine the break-even point. G. Determine the production that maximizes the total profit. Problem 2: A company produces an item at a per-unit cost of $20 and a fixed cost of $1000. The selling price is an exponential function of number of items demanded as follows: p = 60,000e -0.05x, 10 SX S100 A. Determine the profit function. B. Plot the profit versus number of units produced. C. Determine the break-even point. D. Determine the demand that maximizes the total profit. Problem 3: ABC company has to evaluate two cutting machines X and Y. the purchase of an automatic feed machine and a manual feed machine for a finishing process. The information on X and Y are as follows: First cost Salvage Value Life Labor Cost Expected output Maintenance and Operating Cost ($/year) Rate of Return i $70,000 $3,000 8 years $15 per hour 5 pieces per hour $2,000 per year 10% $23,000 $4,000 4 years $17 per hour 4 pieces per hour $3,500 per year 10% How many pieces per year must be finished to justify the higher purchase cost of machine X?

Answer 1

GDP per capita in 2014 GDP per capita in 2010 *100 increase in real GDP per capita GDP per capita in 2010

43032-41615 100 41615

1417 100 41615

Answer 2

GDP per capita in 2014 GDP per capita in 2010 *100 increase in real GDP per capita GDP per capita in 2010

43032-41615 100 41615

1417 100 41615

= 3.41

The average annual growth rate = (Growth in year 2011+ Growth in year 2012 + Growth in year 2013+Growth in year 2014)/ 4

REAL GDP PER CAPITA (2005 PRICES) YEAR 2010 41615 2011 42874 3.03 2012 42184 -1.61 2013 43043 2.04 2014 43032 -0.03

The average annual growth rate

=[3.03+(-1.61)+2.04+(-0.03)]/4

=3.43/4

=0.86