A manufacturer sells 150 tables a month at the price of $200 each. For each $1 decrease in price, he can sell 25 more tables. Each table costs $125 to make.
(a) The demand (price) function is assumed to be linear: p(x) = mx + b, where p is the price of each table and x is the amount of tables produced. Find the expression for the demand function.
(b) The revenue function, R(x) = xp(x), is the revenue generated from selling x tables. Write the expression for the revenue function.
(c) Recall that profit is revenue minus costs. Express monthly profit as a function of the number of tables sold and draw a graph of the profit.
(d) Determine the optimal selling price; i.e. at what price should the tables be sold in order to maximize profit?