Question

Each coffee table produced by Kevin Watson Designers nets the firm a profit of $9. Each bookcase yields a $15 profit. Watson's firm is small and its resources limited. During any given production period (of 1 week) 9 gallons of varnish and14 lengths of high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
The aim of the objective function for Kevin should be to Maximize the objective value.

The optimum solution is: Number of coffee tables produced per week =_____ (round your response to two decimal places).

The optimum solution is: Number of Bookcases produced per week =_____ (round your response to two decimal places).

Answer 1

Let,

x = number of coffee tables produced per week

y = Number of Bookcases produced per week

Objective function is to maximize profit so max 9x + 15y [profit contribution of 1 coffee table is $9 and 1 bookcase is $15]

Subject to,

x+y <= 9 (varnish available per week is 9 gallon and 1 coffee table requires 1 gallon of varnish and 1 bookcase also requires 1 gallon of varnish)

x+2y <=14(14 length of wood is available per week and 1 coffee table requires 1 length of weed and 1 bookcase requires 2 lengths of wood)

x,y >=0 (non-negative constraint)

solving in excel we get,

x = number of coffee tables produced per week = 4

y = Number of Bookcases produced per week = 5

and maximum profit = $111