00:01
For a company that produces and sells x number of units in thousands of an item, the cost of production of a unit per item is $5 and the total fixed cost is $12 ,000.
00:17
The price demand equation is defined by p is equal to 1525 plus minus 20x where p is the price, x is the demand.
00:27
We are to find and interpret the marginal cost function, we are to find the revenue function as a function of x and find its marginal revenue function and we are to determine the number of units that a company must produce and sell to obtain the maximum profit.
00:42
So in this problem, we know the cost of production of an item and the total cost function.
00:49
So we are going to start with the marginal cost function.
00:54
So given the price demand function, for the first question, the marginal cost function will be equal to the variable cost plus the fixed cost which is equal to 5x plus 12 ,000.
01:10
So the cost function c of x will be equal to 5x plus 12 ,000 and the marginal cost function will be equal to d over dx of c of x and this will be equal to d over dx 5x plus 12 ,000 which is equal to 5.
01:36
So the marginal cost function is a constant function.
01:40
So for the second part, the revenue function r of x is given by x p of x is equal to x multiplied by 1525 minus 20x and this is 1525x minus 20x squared...