Math G Spring 2009 Class Handout 3/09

1) In Class Sample Problem on Linear Programming

Mary is installing new storage cabinets in her garage. Two models are available.

Type 1 costs $80 each, requires 6 sq ft floor space and holds 20 cu ft.

Type 2 costs $160 each, requires 8 sq ft floor space and holds 40 cu ft.

Her total budget is $1120 and her garage has 72 sq ft of floor space available.

How can she maximize storage capacity?

2) Homework Problems on Straight Lines Linear Programming

– Show all algebra steps, calculations, explanations.

a. Plot the points (2, 3) (-4, 5) and (0, -3)

b. Plot the graph of the equation 3x – 5y = 12

c. Calculate the slope of the line 4x + 7y = 18

d. Solve the following linear programming problem:

Ian decides to abandon teaching and get into the trail mix manufacturing business to supply all his backpacking friends. He has an initial supply of 1920 ounces of chocolate chips and 1200 ounces of peanuts. He manufactures two different blends called Superchoc and Nuttso, each packaged in a bag.

Each bag of Superchoc contains 12 ounces of chocolate chips and 4 ounces of peanuts

Each bag of Nuttso contains 8 ounces of chocolate chips and 8 ounces of peanuts.

If the profit on each bag of Superchoc is 29 cents and on each bag of Nuttso is 41 cents, use graphs and linear programming to prove how many bags of each blend Ian should manufacture to obtain the maximum profit from his initial supply.