Question

The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the objective function?

Answer 1

The objective function for maximizing profit from selling king and queen beds is Profit (P) = 300x + 150y, where x is the number of king beds and y is the number of queen beds to be sold. This function is subject to budgetary and warehouse space constraints.

Step-by-step explanation:

The objective function in a linear programming problem is the function that needs to be maximized or minimized. In this case, the logistics/operations manager wants to maximize profit from selling king beds (K) and queen beds (Q). Let's denote the number of king beds and queen beds to purchase as x and y, respectively. The profit for each king bed is $300 and for each queen bed is $150.

To write the objective function for maximizing profit, we put the profit per unit times the number of units:

Maximize Profit (P) = 300x + 150y

This function tells us how much total profit will be made from selling x king beds and y queen beds. The manager's constraints are the budget ($75,000) and the warehouse space (18,000 cubic feet), translated into the following inequalities:

1. Cost constraint: 500x + 300y ≤ 75,000
2. Space constraint: 100x + 90y ≤ 18,000

The logistics/operations manager will use these constraints along with the objective function to determine the optimal number of king and queen beds to purchase and store to maximize profit.

Answer 2

As we want to maximize the profit, the objective function is the profit function:

`Profit=300*K+150*Q`

Step-by-step explanation:

This is a linear programming problem.

We want to maximize the profit, and the limitations are budget, where we take into account the cost of the types of beds, and warehouse space, where we take into account the space the beds required.

As we want to maximize the profit, the objective function is the profit function:

`Profit=300*K+150*Q`

The constraints are:

- Budget

`500K+300Q\leq75000`

- Warehouse space:

`100K+90Q\leq 18000`