The metro food services company delivers fresh sandwiches ea

The metro food services company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches---ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 0.48 minutes to assemble, a bologna sandwich requires 0.43 minutes, and a chicken salad sandwich requires 0.46 minutes to make. The company has 11.5 hours of time available each night for sandwich assembly. Vending machine capacity is available for 2,000 sandwiches each day. The selling price for a ham and cheese sandwich is $1.32, the selling price for a bologna sandwich is $1.43, and the selling price for a chicken salad sandwich is $1.38. Customers need a variety of sandwiches available, so metro stocks at least 200 of each. Metro management wants to know the following: a) Using excel solver, how many of each sandwich should they stock? b) If the company could hire a worker and increase the assembly time by 400 minutes, or increase its vending machine capacity by 90 sandwiches, both at no additional cost, which of the two should it do? Why?

Solution

a) Let x,y and z be the number of sandwiches of ham and cheese, bologna and chicken salad sandwich respectively.

According to problem,

          x+y+z <= 2000

Also, 0.48x + 0.43y + 0.46z <= 690 (in minutes)

As every sandwich should have atleast a stock of 200 sandwiches.

Hence, 0.48*200 + 0.43*200 + 0.46*200 = 274 minutes

Remaining time left = 690 - 274 = 416 minutes.

New equations become

x\' + y\' + z\' <= (2000-600)   (200 sandwiches each)

x\' + y\' + z\' <= 1400

and 0.48x\' + 0.43y\' + 0.46z\' <= 416

Converting above equations into seconds, we have

28.8x\' + 25.8y\' + 27.6z\' <= 24960

subject to constraint

Maximize (1.32x\' + 1.43y\' + 1.38z\')

where x\' = x-200, y\' = y-200 and z\' = z-200

With the help of excel solver,

we get y\' = 967, x\' = 0, z\' = 0

Therefore each individual sandwich becomes

Ham and cheese i.e. x = 0 +200 = 200

Bologna i.e. y = 967 + 200 = 1167

Chicken salad i.e. z = 0 + 200 = 200

Total number of sandwiches i.e. x+y+z = 1567

b) Now total number of sandwiches is 1567, but the vending machine capacity is 2000. Hence, we need to increase the assembly time so that we can make more sandwiches. Hence, the option is of the company could hire a worker and increase the assembly time by 400 minutes.