XYZ company plans to market a new product. based on its market studies, the company estimates that it can sell 5500 units in 2004. the selling price will be $2 per unit. variable costs are estimated to be 40% of the selling price. fixed costs are estimated to be $6000. develop the revanue, cost and profit functions in terms of sales and quantity.
revenue = units * price/unit
r = 2x for x units
var cost = .2r
fix cost = 6400
total cost c = 6400 + .2(2x)
total revenue = 2x
breakeven when cost = revenue
2x = 6400 + .4x
1.6x = 6400
x = 4000
so, at 4000 units,
revenue = 8000
cost = 6400 + .2(8000) = 8000
Just use the formula
To develop the revenue, cost, and profit functions in terms of sales and quantity, we need to consider the given information:
Selling Price per unit: $2
Variable Costs (as a percentage of selling price): 40%
Fixed Costs: $6000
Estimated Sales Quantity: 5500 units in 2004
Revenue:
The revenue function refers to the total amount of money obtained from selling a certain quantity of products.
Revenue = Selling Price per unit * Sales Quantity
So, revenue function (R) in terms of sales quantity (Q) can be expressed as:
R(Q) = $2 * Q
Costs:
There are two types of costs to consider: variable costs and fixed costs.
Variable Costs:
Variable costs change depending on the quantity of products sold. In this case, they are estimated to be 40% of the selling price.
Variable Cost per unit = 40% of $2 = $0.8
Variable costs function (VC) in terms of sales quantity (Q) can be expressed as:
VC(Q) = Variable Cost per unit * Q
Fixed Costs:
Fixed costs remain constant regardless of the quantity of products sold. In this case, fixed costs are estimated to be $6000.
Costs function (C) in terms of sales quantity (Q) can be expressed as:
C(Q) = Fixed Costs + Variable Costs
C(Q) = $6000 + $0.8 * Q
Profit:
Profit is the difference between revenue and costs. Profit function (P) in terms of sales quantity (Q) can be expressed as:
P(Q) = R(Q) - C(Q)
P(Q) = $2 * Q - ($6000 + $0.8 * Q)
Simplifying the equation further, we have:
P(Q) = $2Q - $6000 - $0.8Q
P(Q) = $1.2Q - $6000
Therefore, the revenue function (R), cost function (C), and profit function (P) in terms of sales quantity (Q) are as follows:
R(Q) = $2Q
C(Q) = $6000 + $0.8Q
P(Q) = $1.2Q - $6000
To develop the revenue, cost, and profit functions in terms of sales and quantity, we need to understand the different components involved.
1. Revenue function:
The revenue generated is the total income from selling the product. It can be calculated by multiplying the quantity sold with the selling price per unit. In this case, the selling price is $2 per unit, and the quantity sold is 5500 units. Therefore, the revenue function can be expressed as:
Revenue = Quantity Sold * Selling Price = Q * P
where Q is the quantity sold and P is the selling price per unit.
2. Cost function:
The cost includes both variable costs and fixed costs. Variable costs are estimated to be 40% of the selling price. Therefore, the variable cost per unit can be calculated as 40% of $2, which is $0.80. The variable cost function can be expressed as:
Variable Cost = Variable Cost per unit * Quantity Sold = VC * Q
where VC is the variable cost per unit and Q is the quantity sold.
Fixed costs are estimated to be $6000 and remain constant regardless of the quantity sold. Hence, the fixed cost function is simply:
Fixed Cost = $6000
3. Profit function:
Profit is calculated by subtracting the total cost from the total revenue. Therefore, the profit function can be expressed as:
Profit = Revenue - Cost = (Q * P) - (VC * Q + Fixed Cost)
= Q * (P - VC) - Fixed Cost
Combining the above functions, we get:
Revenue function: Revenue = Q * P
Cost function: Cost = VC * Q + Fixed Cost
Profit function: Profit = Q * (P - VC) - Fixed Cost
So, to calculate the revenue, cost, and profit for a given quantity (Q), you can use these equations by substituting the appropriate values for the selling price per unit (P), variable cost per unit (VC), and fixed cost (Fixed Cost).