1. Professor Simpleton has a dilemma. A double dose of artic air is spilling into North Texas, and he needs to keep his garage apartment/office warm for four (4) days by burning wood in his wood stove. He has a limited supply of hickory, red oak, and birch logs to get him through the cold spell. The logs are of a standard size, but each log costs a different amount and puts out a different amount of heat when it is burned (measured in thousands of BTU's).

Log Type	Cost (per log)	BTU's (in 1000's)	Availability (logs)
Hickory (H)	$1.60	28	16
Red Oak (R)	$1.50	24	30
Birch (B)	$1.27	20	20

Based on the weather forecast provided by WFAA and Staff Meteorologist Pete Delkus, he has calculated he will need to burn at least 131 (measured in 1000's) BTU's on day 1, 180 on day 2, 127 on day 3, and 216 on day 4.

A. Devise an optimal burning schedule for these 4 days that minimizes cost. You cannot burn a fraction of a log because Professor Simpleton doesn't own a log splitter.

B. Suppose the red oak comes in sacks of 15 logs, and the birch comes in sacks of 10 logs. Professor Simpleton decides that if he burns any red oak, he wants to burn at least one full sack; and if he burns any birch, he wants to burn at least one full sack (he does not need to burn any full sacks of either kind thereafter). Revise your model in part A and devise a new optimal burn schedule.