In this fictitious example, you are a pharmaceutical analyst considering two different vaccines, Vaccine A and Vaccine B. As you can see in the attached workbook, both vaccines have different administration costs. Vaccine A costs $22 to administer. Vaccine B costs $13 to administer. The number of shots of each vaccine are also subject to constraints, where the maximum number of Vaccine A that can be administered is 1000, and the maximum number of Vaccine B is 750. Further, the number of Vaccine A to be administered must be less than or equal to Vaccine B. Using the attached workbook, solve for the number of Vaccine A and Vaccine B to administer with the objective of maximizing net profit. What is your resulting net profit?

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ahmadfardeen571 ahmadfardeen571 · Answer 1 · 2022-07-19T19:55:50+02:00

Profit maximising total cost is $22000.

The question says, 'maximize the profit', but per unit, profit figures are not given, only per unit.

Cost is given. So, we will assume that minimizing total cost is equivalent to maximizing total profit.

Let the number of vaccines administered be x for Vaccine A and y for Vaccine B. Then,

Total cost, z = 22x + 13y. This is the objective function

Constraints:

Number of Vaccine A administered must be less than 1000 => x < 1000.

The number of Vaccine B administered must be less than 750 => y < 750

The number of Vaccine A administered must be less than the number of Vaccine B administered => x <

Naturally, both x and y must be non-negative.

Thus, the Linear Programming Problem is:

Minimize z = 22x + 13y

Subject to

x < 1000

y < 750

x<y

x, y z C

The last constraint => the points to be considered are confined to the first quadrant.

x < 1000 covers all points to the left of the line parallel to the y-axis at a distance of 1000 units to the

right of the y-axis.

y < 750 covers all points below the line parallel to the x-axis at a distance of 750 units above the x-axis.

x < y covers all points below the 45 line.

Thus, the feasible region is bounded by the polygon OPQRO, where, O is the origin, P(750, 750) is

The point at which the 450 line intersects the line y = 750, Q(1000, 750) is the point at which the line x

= 1000 intersects the line y = 750 and R(1000, 0) is the point at which the line y = 750 intersects the

X-axis

Substituting the coordinates of these points in the objective function, z = 22x + 13y, we have:

Zo = 0; Zp = 26250; zo = 31750; and ZR = 22000

Clearly, ZR = 22000 is the minimum

Thus, profit maximising total cost is $22000.

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