Question

SHOW STEP BY STEP SPREADSHEET MODEL

A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table:

Machine	Country	Contemporary	Total Machine Time Available Per Week
Router	2.5	3.0	1,000
Sander	3.5	5.5	2,000
Polisher	2.0	1.0	1,500

Country tables sell for $395 and contemporary tables sell for $515.   Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue?

1. Formulate an LP model for this problem
2. Create the spreadsheet model and use Solver to solve the problem.

Answer 1

Let,

x1 =number of country tables to make and x2 = number of contemporary tables to make

Objective is to maximize revenue => Z = Max 395x1+515x2

subject to,

(Router) 2.5x2 +3x2 <= 1000
(Sander) 3.5x1 + 5.5x2 <= 2000
(Polisher) 2x1 + 1x2 <= 1500

(Min country) 0.75x1-0.25x2 >= 0

(Min contemporary)-0.38x1+0.62x2 >= 0

x1,x2 >= 0
Solving in solver we get,

Optimal solution :

Country table : 86.95652174 (Answer is 87 is rounding is required)
Contemporary table : 260.8695652 (Answer is 261 if rounding is required)

maximized revenue = 168695.6522

Solver screenshot

Solver formula

Solver window