1. A Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month's production output. The table Below shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer.A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer. Formulate a linear programming model for this problem.

Unit shipping cost

From/to Customer 1 Customer 2 Customer 3 Output

Factory 1 $600 $800 $700 400 units

Factory 2 $400 $900 $600 500 units

Order size 300 units 200 units 400 units

Define the variable used:

LP Model:

Identify the feasible region:

Corner Points and the objective functions:

Optimal solution:

2. A certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. The data for the radiation therapy is given below:

Fraction of doseabsorbed per sec Average dosage

Area Beam 1 Beam 2 (in kilorads)

Brain 0.4 0.5

Spine 0.3 0.1 At most 2.7

Tumor 0.5 0.5 At most 6

Center of tumor 0.6 0.4 At least 6

Determine the optimal exposure times for beam 1 and 2.

Define the variable used:

LP Model:

Identify the feasible region:

Corner Points and the objective functions:

Optimal Solution (final answer):

3. This pandemic, Abheedette learned to bake while on home quarantine.She also realized that she will be able to make P60.00 profit per tray of banana muffins and P120.00 profit per tray of blueberry muffins.She needs 2 cups of milk and 3 cups of flour to bake a tray of banana muffins.And, baking a tray of blueberry muffins takes 4 cups of milk and 3 cups of flour.She has 16 cups of milk and 15 cups of flour. How many trays of each flavor must be baked to maximize the profit?

Define the variable used:

LP Model:

Identify the feasible region:

Corner Points and the objective functions:

Optimal Solution (final answer):