Question

Sandra Swere is the owner of Totes For All (TFA), a home-based company that makes tote bags to sell at craft fairs around the country. There are two styles of bags: Flower Power and Butterfly Dream.

Flower Power bags are sold for $115 each and Butterfly Dreams are sold for $105 each.

TFA has two workers who actually make the bags.

Worker A makes the Flower Power bags, can complete one bag in 2 hours and charges $10 per hour to do the work. Worker A is available for a maximum of 50 hours during the next week.

Worker B produces each Butterfly Dream bag in 1.2 hours, charges $13 per hour and can work 35 hours next week.

The following table provides additional information about materials required for each style of bag. TFA has 100 yds of canvas and 150 ounces of metal available for the manufacture of the bags.

Canvas costs $12.50 per square yard, the metal costs $5.50 per ounce.

Style	Canvas required (sq. yds per bag)	Metal required (oz per bag)
Flower Power	2.25	5
Butterfly Dream	2.4	7

Write the LP formulation to determine how many of each style of bag should be produced next week to maximize the PROFIT for TFA.

Answer 1

Decision variables:

x = Number of Flower Power bags to be made

y = Number of Butterfly Dream bags to be made

z = Profit (in $)

Objective function

Total revenue earned = 115x + 105y

Worker A works for 2x hours and charges 10 per hour, so his charges are 20x

Worker B works for 1.2y hours and charges 13 per hour, so his charges are 15.6y

Cost of canvas required is (2.25x + 2.4y) * 12.50 = 28.125x + 30y

Cost of metal required is (5x + 7y) * 5.50 = 27.5x + 38.5y

Total cost = 20x + 15.6y + 28.125x + 30y + 27.5x + 38.5y = 75.625x + 84.1y

Profit = Revenue – Cost = (115x + 105y) – (75.625x + 84.1y) = 39.375x + 20.9y

So, the objective function is maximize z = 39.375x + 20.9y

Constraints:

2x ≤ 50, so x ≤ 25 [Worker A hours]

1.2y ≤ 35, so y ≤ 29.1667 [Worker B hours]

2.25x + 2.4y ≤ 100 [Canvas]

5x + 7y ≤ 150 [Metal]

x, y ≥ 0 and integers

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