Question

Pamplin PCs is a computer retail store that sells three kinds of personal computers: traditional desktops, business-oriented laptops and mobile tablets. The computers that Pamplin PCs sells are manufactured by WolfConn. WolfConn, due to current demand from other retail computer store customers, cannot ship more than 80 desktops and 75 laptops to Pamplin PCs in the next month. However, Wolf Conn requires that Pamplin PCs order a minimum of 50 tablets. Pamplin PCs must spend 1 hour of labor to setup desktops computers. 3 hours of labor to setup laptop computers, and 2 hours of labor to setup tablets. The company expects to have a limit of 300 hours available for computer setups during the next month. The company earns a net profit of $625 for the desktops, $900 for the laptop, and $500 for the tablet. The company is sure it can sell all the computers they order. How many of each model should the company order?

Answer 1

The company should use linear programming to maximize profits for ordering desktops, laptops, and tablets within the constraints of shipping limitations, minimum order requirements, and available labor hours. Labor hours for setup are 1 hour for desktops, 3 hours for laptops, and 2 hours for tablets, with profits being $625, $900, and $500 respectively.

Step-by-step explanation:

The question posed is a linear optimization problem that can be solved with linear programming to maximize profits subject to given constraints. We need to find out how many desktops, laptops, and tablets the company should order considering the limitations posed by WolfConn's shipping capabilities and the labor hours available, as well as maintaining profitability through net profits from each type of computer.

The constraints include the shipping limitations (80 desktops and 75 laptops), the minimum order of 50 tablets, and the total available labor hours (300 hours). Additionally, labor setup time per desktop is 1 hour, 3 hours for laptops, and 2 hours for tablets. Net profits for Pamplin PCs are $625 for each desktop, $900 for laptops, and $500 for tablets.

To determine the optimal number of each model to maximize profit, each variable (desktops, laptops, tablets) will be assigned a profitability coefficient based on the net profit per item, and the problem will be formulated to ensure that the total setup hours do not exceed the maximum allowed, while also satisfying shipping and minimum order requirements. This is typically solved through methods like the simplex algorithm or by using software that handles linear programming problems.