DVD player

As a marketing department team#4 our primary goal is to make best estimate the price for our new product “DVD player” that will produce the maximum 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;

² The demand for a new DVD player on the national market.

² The cost of production of a new DVD player.

² The revenue in relation to quantity sold.

² The price that is likely to maximize profit.

² How profit changes in response to changes in quantity of DVD players.

² The level of production that will maximize our profit.

Here, we have presented our analysis by using mathematical tools to compute required information.

Cost data:

To produce new DVD player, the first 400,000 units will have production cost of $41.00 per unit. The next 200,000 units will cost $31.00 per unit to produce. After the first 600,000 units can be produced for 23.00 further up to 1,300,000. Also there are fixed overhead costs of $40,800,000 before producing any players.

Given the information, we set up the cost function which tells us the total 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 the cost function is if q 400,000. Second part of the function was set up by plugging the number where and variable cost $31.00 to the equation and found out y-axis of the second piecewise function and then it came out 31q +44,800,000 if 400,000 < q 600,000. The last piece of the function is I basically did same thing as the second one by plugging the number where and variable cost $23.00 to get y-axis of the function and came out 23q+49,600,000 if 600,000<q 1,300,000.

Finally, we got piecewise cost function as below and the graph shows how much it cost to produce q unit.