A local office supply store wants to determine the optimal amount to produce of

Question

A local office supply store wants to determine the optimal amount to produce of its two most popular selling staplers, the Economy Model & the Travel Model in order to maximize its profits. The store makes $5 profit on every Economy Model and $6 on every Travel Model. While the store would like to cam- an unlimited amount of each stapler, it is limited by a cost restriction, space constraint and a stocking fame requirement. The Economy Model costs $2 for every unit and the Travel Model costs $3 for every unit & the office supply store has at most $240 to spend on both stapler models. Once the product is at the store, it takes an employee 2 minutes to stock each Economy Model and 1 minute to stock each Travel Model and the employee has no more than 120 minutes available to stock both stapler models. Additionally the store only has the space to stock 40 units of the Travel Model. What is the optimal amount that should be produced of both stapler models if the office supply store wants to maximize its profits? (60, 30) (0, 80) (40, 40) (30, 60) (60, 0)

Explanation / Answer

Below is the formulation of the given problem,

Max. Profit = 5x + 6y

Constraints,
2x + 3y <= 240
2x + y <= 100
y <= 40

Solving the above formulated problem using excel solver gives

x = 40 and y=40

Hence option C

Solver Solution x y Total Demand Decision Variables 40 40 Profits 5 6 440 Constraint 1 2 3 200 240 Constraint 2 2 1 120 120 Constraint 3 0 1 40 40

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