Each coffee table produced by Timothy Kent Designers nets th

Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent\'s firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 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.

Referring to Table 8-3, suppose that this problem requires that you use all the varnish for the week. How would the linear programming representation change?

Select one:

a. None of these

b. 1B + 1T <- 10 will become 1B + 1T <- 12.

c. 2B + 1T  <- 12 will become 2B + 1T = 12.

d. 1B + 1T <- 10 will become 1B + 1T = 10.

e. 1B + 1T  <- 10 will be replaced by 1B + 1T >- 10.

Solution

We know that a single coffee table ( number of coffee tables= T) requires 1 gallon of varnish and a single book case (no of bookcases= B) requires 1 gallong of varnish.
Now before the constaints was added we could have used up the whole of 10 gallons of garnish or only a part of it which means <10 gallons of varnish. So the earlier representation in linear programming terms would be:
1B+1T <= 10 (coefficient of B and T is 1 becuase each bookcase and each table will require 1 gallon of varnish)

After the change of criterion when it became necessary that all varnish for the week is used by; you have to have exactly 10 gallons used by in making coffee table and book cases so now the representation in linear programming terms would become:
1B+1T = 10; As the inequality gets removed because all 10 litres of varnish has to be used up;

So correct answer choice is \'d\' which is B + 1T <- 10 will become 1B + 1T = 10.