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Part II: Describing Constraints For each situation, write down the appropriate c

ID: 332265 • Letter: P

Question

Part II: Describing Constraints For each situation, write down the appropriate constraint. Please use the standard symbols"+" and"-" for plus and minus, and " for multiplication; however, if you find the symbols "s' and "2" difficult to keep straight, you may write "LE" for "Less than or equal to," and"GE for Greater than or equal to Example: An office is buying filing cabinets. The Model A cabinet holds a maximum of 3 cubic feet of files. Model B holds a maximum of 4.5 cubic feet of files. At any time, the office will have a maximum of 17 cubic feet of files that need to be stored. (A bit more cabinet space wouldn't be a problem, but not enough would be. The files can't be stacked on the floor.) Write a constraint on the number of cabinets the office should acquire A - number of Model A cabinets purchased B number of Model B cabinets purchased Answer: AT 3 cubic feet) + B"(4.5 cubic feet) 17 cubic feet A 3 cubic feet) B (4.5 cubic feet) GE 17 cubic feet 1. Patty makes pottery in her home studio. She works a total of six hours (360 minutes) per day. It takes her 10 minutes to make a cup, 15 minutes to make a bowl, and 30 minutes to make a vase. Write a constraint governing the joint production of cups, bowls and vases in a day. (Trans: "joint determined together, each affected by the others.) Variables C number of cups made B = number of bowls made V number of vases made 2. An aid agency is buying generators for storm survivors. The generators will be shipped on a convoy of flatbed trucks having a total usable cargo area of 1,350 square feet. Generator A has a footprint (floor space required) of 8 square feet, and Generator B has a footprint of 12 square feet. VWrite a constraint governing the number of generators of each type than can be shipped

Explanation / Answer

Ans 1)

Total minutes available per day = 360

Time taken to make a cup = 10 minutes

Time taken to make a bowl = 15 minutes

Time taken to make a vase = 30 minutes

If,

C = number of cups made

B = number of bowls made

V = number of vases made

CONSTRAINT

10*C + 15*B + 30*V <=360

Ans 2)

Total usable cargo area = 1350 feet2

Footprint of generator A = 8 feet2

Footprint of generator B = 12 feet2

If,

GenA =number of A type generators shipped

GenB =number of B type generators shipped

CONSTRAINT

8*GenA + 12*GenB <= 1350

Ans 3)

Profit per cup = $0.75

Profit per bowl = $2.40

Profit per vase = $1.35

OPTIMAL FUNCTION

Z = 0.75*C + 2.40*B + 1.35*V