2. A group of young students earn a steady living by picking up discounted items
ID: 391107 • Letter: 2
Question
2. A group of young students earn a steady living by picking up discounted items from a used electronics store for 10S a piece and reselling them. Each item has a street value, a weight and a volume; there are limits on the number of available items (as shown). A total weight of 500 lbs and a total volume of 300 cu. ft. can be transported in one attempt. Item value(S) weight (Ibs) volume (cu. ft.) availability TV 40 Laptop 50 Monitor 120 30 10 20 20 30 15 (a) (points: 3.5) Formulate a LP problem to find how many of each items should the students pick for reselling. b) (points: 6) Solve it using the simplex method in tabular form showing the intermediate steps. What is the optimal solution and the optimal objective value?Explanation / Answer
Decision variable:
T = units of TV to be purchased
L = units of laptops
M = units of monitors
Objective function:
Maximize the total profit by purchasing units.
Profit = (street value - purchased value)*quantity
Max z = (40 -10)T + (50-10)L + (120-10)M
Max z = 30T + 40L + 110M
Subjected to:
Weight constraint:
Total Weight of purchased items should less than or equal to 500 lbs
30T + 10L + 20M <= 500
Volume constraint:
Total volume to be purchased should be less than 300 cu.ft.
8T + 5L + 4M <= 300
Availability items constraint:
TV availability: T <= 20
Laptop avail. L <= 30
Monitor avail. M <= 15
Nonnegativity constraint: T,L,M >= 0
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