Question

Problem 2

The manager of the deli section of a grocery superstore has just learned that the department has 112 pounds of mayonnaise, of which 70 pounds is approaching its expiration date and must be used. To use up the mayonnaise, the manager has decided to prepare two items: a ham spread and a deli spread. Each pan of the ham spread will require 2.8 pounds of mayonnaise, and each pan of the deli spread will require 2.0 pounds. The manager has received an order for 10 pans of ham spread and 8 pans of the deli spread. In addition, the manager has decided to have at least 10 pans of each spread available for sale. Both spreads will cost $3 per pan to make, but ham spread sells for $6 per pan and deli spread sells for $7 per pan. Convert this word problem into an LP model.

Hint: Note that there are two objective functions. One would be where you maximize your profits. The other objective function is to minimize costs. The constraints remain the same for both objective functions. You will NOT be solving this problem. You will only be writing the LP model i.e., the objective functions and the set of all constraints.

Answer 1

The company can have two objectives in this case. i.e. it can reduce the overall cost and maximize the total profits

Let x denote ham and y denote deli

Objective 1:

Minimize z (cost) = 3x + 3y

Order received = 10 pans of ham spread and 8 pans of the deli spread

At least 10 of each spread must be sold

This makes at least 18 of one kind n total and 20 of another in total should be sold.

Thus,

Subject to

2.8x +2y >= 70

X >= 20

Y >= 18

X, y >=0

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Objective 2:

From the question:

Profit for x = (6 – 3) = $3

Profit for y = (7 – 3 ) =$4

Maximize profit = 3x + 4y

Subject to

2.8x +2y <= 112

X >= 20

Y >= 18

X, y >=0

hope this helps. please upvote if it helped.