A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 60 hours of labor and 120 units of lumber. Wren houses yield a profit of $6 each, and bluebird houses yield a profit of $15 each. a) Write out the objective and constraints. b) Solve graphically.

a) 6W+15B

subject to:

4W+2B ≤ 60

4W + 12B≤ 120

W>0

B>0

b) see attachment

Explanation:

a) W: wren birdhouse

B: bluebird house

Objective function:

6W+15B

Explicit constraints:

4W+2B ≤ 60

4W + 12B≤ 120

Implicit constraints

W>0

B>0

b)  coordinates of optimal region:

(0,0), (0,10), (12,6), (15,0)

For optimum profit:

(0,0): 6(0) + 15(0)= 0

(0,10): 6(0) + 15(10)= 150

(12,6): 6(12) + 15(6)= 162

(15,0): 6(15) + 15(0)= 90

Optimal solution is: (12,6) or 12 wren birdhouse and 6 bluebird house

c

explanation:

c because the item on a bank statement is also referred to as an account statement. in addition, it provides the beginning balance, ending balance, statement date, transaction date for each transaction, payee, customer name and address, statement period, the account holder's account number, and the bank's customer service number