Question

A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as:

[ {Price} = 150 - 0.01 × {Demand for an annual printing of this particular product.} ]
The company is planning its productions for the year 2021. The company is considering the production of a certain number of 2,000 pages units. In 2019 the company had produced 4 similar units but with fewer pages count per unit (1,200; 1,400; 1800; and 1,900), and the material costs associated with those 4 units are (14.15 JD, 15.65 JD, 18.25 JD, and 18.90 JD respectively). The material cost index values were 185 for 2018, 193 for 2019, 200 for 2020, and 206 for 2021). The fixed costs per year (i.e., per printing) = 50,000 JD, and the variable cost will consist of the material cost and the labor cost.
The company started to produce 2000 pages unit in 2021, and the project management team observed that 8.23 labor hours were needed to produce the first unit; however, the number of labor hours per unit decreased thereafter at an 80% learning slope. Use the 6th unit as the basis for estimating the average labor hours per unit and assume the 2021 average labor wage is 4.0 JD per hour.
(a) What is the range of profitable demand?
(b) At what demand the company will ensure the maximum profit that can be achieved if the maximum expected demand is 6,000 units per year? (How many units should the company produce in 2021 in order to maximize its profit?)
(c) Based on the demand identified in part (b), what is the breakeven selling price per unit?
(d) Based on the demand identified in part (b), what is the selling price per unit?
(e) How much profit will the company make in 2021 using the optimal demand?

Answer 1

To determine the range of profitable demand, calculate the revenue and cost functions and solve the inequality Revenue > Cost. To find the demand that maximizes profit, determine the profit function and find its maximum value. Calculate the breakeven selling price per unit and the selling price per unit based on the demand identified. Find the profit for 2021 by multiplying the profit per unit by the quantity demanded.

Step-by-step explanation:

The range of profitable demand can be determined by calculating the range of demand values for which the company's revenue exceeds its total cost. To do this, we need to determine the revenue and cost functions. The revenue function can be calculated by multiplying the price per unit by the quantity demanded, while the cost function can be calculated by adding the fixed costs to the variable costs.

Once we have the revenue and cost functions, we can find the range of profitable demand by solving the inequality: Revenue > Cost. The demand values that satisfy this inequality represent the range of profitable demand.

To find the demand at which the company will ensure the maximum profit, we need to determine the profit function, which is calculated by subtracting the cost function from the revenue function. We can then find the maximum value of the profit function to identify the demand value that maximizes profit.

The breakeven selling price per unit can be calculated by setting the revenue equal to the cost and solving for the price per unit. Similarly, the selling price per unit can be determined by substituting the demand value from part (b) into the revenue function and solving for the price per unit.

The profit for 2021 can be calculated by multiplying the profit per unit (obtained from the profit function) by the quantity demanded identified in part (b).