As a marketing department team#4 our primary goal is to make bestestimate the price for our new product “DVD player” that will produce themaximum profit and how many of the DVD players that we can expect to sell,and how much profit we might hope to realize from the sales. In order to price DVD player, we need to estimate;< The demand for a new DVD player on the national market. < The cost of production of a new DVD player. < The revenue in relation to quantity sold.
< The price that is likely to maximize profit. < How profit changes in response to changes in quantity of DVD players. < The level of production that will maximize our profit. Here, we have presented our analysis by using mathematical tools tocompute required information.
Cost data:To produce new DVD player, the first 400,000 units will have productioncost of $41. 00 per unit. The next 200,000 units will cost $31. 00 per unitto produce.
After the first 600,000 units can be produced for 23. 00 furtherup to 1,300,000. Also there are fixed overhead costs of $40,800,000 beforeproducing any players. Given the information, we set up the cost function which tells us thetotal costs at any level or production q units. First, let q be the number of units be specified by the variable and C(q)be the total cost function.
The Cost function is set up by formula; C(q)=Variable Costs + Fixed Costs. Given the data, up to 400,000 units are produced, our first piece of thecost function is picif q pic400,000. Second part of the function wasset up by plugging the number where pic and variable cost $31. 00 to theequation and found out y-axis of the second piecewise function and then itcame out31q +44,800,000 if 400,000 < q pic 600,000. The last piece ofthe function is I basically did same thing as the second one by pluggingthe number where picand variable cost $23.00 to get y-axis of thefunction and came out 23q+49,600,000 if 600,000