Business Applications typically found in RIT’sAlgebra for Mgmt. Science (1016-225) and Calculus for Mgmt. Science (1016-226)

I.

Total Revenue, Total Cost, Total Profit a. Total Revenue (R) from the sale of x units = R(x): R(x) = (price per unit)(# of units)

R(x) = (price per unit)(x)

b. Total Cost (C) of production and sale of x units = C(x): C(x) = (cost per unit)(x) + fixed costs Total cost is made up of 2 parts: 1. fixed costs (e.g. rent, utilities, etc) 2. variable costs (costs directly related to the number of units produced) c. Total Profit (P) from the production and sale of x units = P(x): P(x) = R(x) – C(x) Total profit is the difference between the amount received from sales (revenue) and cost of production. II. Marginal Revenue, Marginal Cost, and Marginal Profit a. Marginal Revenue MR

( )

1. If R(x) is linear, then MR is the slope of the revenue function. 2. Calculus for Management Science: MR is the derivative of the revenue function b. Marginal Cost MC

( ) ( )

1. If C(x) is linear, then MC is the slope of the cost function. 2. Calculus for Management Science: MC is the derivative of the cost function
III.

a. Marginal Profit MP

1. If P(x) is linear, then MP is the slope of the profit function. 2. Calculus for Management Science: MP is the derivative of the profit function IV. Break Even Point a. The point at which the revenue equals the cost: which is another way of saying…

Find x such that R(x) = C(x) Find x such that P(x) = 0

The point at which profit equals zero:

b. When the revenue function is greater than the cost function, there is a profit: R ( x) > C ( x)

c. When the cost function is greater than the revenue function, there is a loss: C ( x) > R( x)
V. Supply, Demand and Market Equilibrium a. p = price and q = quantity b. The law of supply states that the quantity supplied for sale will increase as