solution

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 x 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?)

(e) 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?