Question

An appliance dealer wants to purchase a combined total of no more than 200 vacuum cleaners, refrigerators and dishwashers for inventory. Vacuum cleaners weigh 50 pounds each, refrigerators weigh 380 pounds each and dishwashers weigh 120 pounds each. Suppose that the dealer is limited to a total of 16,000 pounds for these three items. There is a profit of $15 for each vacuum cleaner, $70 for each refrigerator and $30 on each dishwasher.

Answer 1

Given problem can be solved using Linear Programming concept of Operations Research.

Variable definition:

x = Number of vacuum cleaners

y = Number of Refrigerator

z = Number of Dishwasher

Objective Function

Dealer would want to maximize his/her profit.

Profit = 15*x + 70*y + 30*z

Therefore,

Maximize Z = 15*x + 70*y + 30*z

Constraints:

x + y + z <=200 ..........Constraint as there's limit on total inventory

50*x + 380*y + 120*z <=16000 ..........Constraint as there's a limit on inventory weight

x,y,z>=0 .............Non-negativity constraint as number of appliance cannot be zero.

x, y, z should be integers.

Solving using Excel

Formulated in excel as belows

Formula shown below:

Now solve using solver function from the Data tab in the menu bar:

1. Set objective as shown in the figure below to MAX

2. Add constraints as shown in the figure below from clicking the Add button on right side of solver window

3. Set the solving method to Simplex LP

4. Click Solve

Following is the result summary generated in excel.

Therefore Dealer should by 115 Vacuum cleaners and 85 Dishwashers.