What would be the inequality for this situation?

Question

An electronics company has hired you to determine how to spend its production budget. The goal of the company is to minimize the cost of production. The number of each type of smartphone docking stations you choose is critical to the success of the company and its profit. The challenge of selecting the right amount of each type of docking station is not just cost, but also the people’s demand for each docking station. The company provides you with the following information:



1. The company can produce a minimum of 600 units and a maximum of 1500 units per shift of basic docking stations. 

1. The company will produce a minimum of 800 units and a maximum of 1700 units per shift of multifunction docking stations. 

1. They must produce at least 2000 items per shift to keep up with demand. 

1. Each basic docking station costs $55 and each multifunction docking station costs $95 per unit to make. 

Answer 1

Let b = basic docking station units

Let m = multifunction docking station units

The company can produce a minimum of 600 units and a maximum of 1500 units per shift of basic docking stations.

600 ≤ b ≤ 1500

The company will produce a minimum of 800 units and a maximum of 1700 units per shift of multifunction docking stations.

800 ≤ m ≤ 1700

They must produce at least 2000 items per shift to keep up with demand.

b + m ≥ 2000

Each basic docking station costs $55 and each multifunction docking station costs $95 per unit to make.

cost = $55b + $95m

Since the unit cost for the basic docking station is much less than the multifunction docking station, to minimize cost, they want to maximize the number of basic docking stations and minimize the number of multifunction docking stations.

If they were to strictly maximize the number of basic docking stations, they can produce 1500 units. Since the number of basic and multifunction docking stations need to be at least 2000, that means the number of multifunction docking stations must be at least 500 units. However, this is less than the minimum number of multifunction docking station units that can be produced. Instead, let's go with the minimum number of multifunction docking stations, which is 800 units. To achieve the necessary number of 2000 total units, the number of basic docking functions needs to be at least 1200 units.

So to minimize cost, they should produce at least 1200 basic docking stations and 800 multifunction docking stations.