Engineering estimates show that the variable cost of manufacturing a new product will be $35 per unit. Based on market research, the selling price of the product is to be $120 per unit and variable selling expense is expected to be $15 per unit. The fixed costs applicable to the new product are estimated to be $2800 per period and capacity per period is 100 units.

Show an algebraic expression of the revenue function and the cost function.

2800

To express the revenue function and the cost function algebraically, we need to understand the components involved.

1. Revenue Function:
The revenue is obtained by multiplying the selling price by the number of units sold. Since the number of units sold can vary, we'll represent it as 'x' in our equation.

Revenue = Selling Price * Number of Units Sold

In this case, the selling price is $120 per unit, so the revenue function can be expressed as follows:

Revenue = 120x

2. Cost Function:
The cost consists of both fixed costs and variable costs. Fixed costs remain constant regardless of the number of units produced or sold, while variable costs change based on the number of units.

The fixed costs are estimated to be $2800 per period, so the fixed cost function can be represented as follows:

Fixed Cost = $2800

The variable costs include both the manufacturing variable cost and the variable selling expense. In this case, the manufacturing variable cost is given as $35 per unit, and the variable selling expense is given as $15 per unit.

Variable Cost = Manufacturing Variable Cost + Variable Selling Expense
Variable Cost = $35x + $15x

Now, to obtain the overall cost function, we'll sum up the fixed cost and the variable cost:

Cost = Fixed Cost + Variable Cost
Cost = $2800 + ($35x + $15x)

Simplifying the expression further, we get the cost function as follows:

Cost = $2800 + $50x

Thus, the algebraic expression for the revenue function is Revenue = 120x, and the algebraic expression for the cost function is Cost = $2800 + $50x.

The revenue function is the product of the selling price and the number of units sold. Since we don't have information about the number of units sold, let's represent it as "x".

Revenue function:
Revenue = Selling price * Number of units sold
Revenue = $120x

The cost function is the sum of the variable cost of manufacturing, variable selling expense, and fixed costs.

Cost function:
Cost = Variable cost of manufacturing + Variable selling expense + Fixed costs
Cost = $35x + $15x + $2800
Cost = $50x + $2800