In andrew’s furniture shop, he builds bookshelves and tables. each type of furniture takes him about the same time to make. he figures he has time to make, at most, 25 pieces of furniture by this saturday. the materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. he has $675.00 to spend on materials. andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. how many of each piece of furniture should andrew make to maximize profit?

18 bookshelves and 7 table Andrew should make to maximize profit

Step-by-step explanation:

Given:

Cost to build a bookshelf = $20

Cost to build a table = $45

Amount available to spend = $675

Let x be number of bookshelves built.

Let y be number of tables built.

The total number of bookshelves and tables = 25

⇒x + y = 25   --1

The total amount available to build x bookshelves and y tables = $675

⇒20x + 45y = 675

dividing through by 5

⇒4x + 9y = 135      2

Substitute value of y from (1) into (2).

4x + 9(25 - x) = 135

4x + 225 - 9x = 135

-5x = -90

 x = 18

From (1),obtain

 y = 25-18= 7

The profit is $60 per bookshelf and $100 per table.

The profit = 18*60 + 7*100 =  $1780

So, 18 bookshelves and 7 table Andrew should make to maximize profit.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2