Question

A beverage can manufacturer makes three sizes of soft drink cans—Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 105 production hours per day, and the daily supply of metal, no more than 200 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size.

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Cans
	Large	Medium	Small	Maximum
Metal (kg)/batch	9	6	5	200
Machines’ Time (hr)/batch	4.4	4.2	4	105
Profit/batch	$51	$40	$42

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a. Develop a linear programming model by identifying the variables, writing the objective function

b. Write all necessary constraints

c. Find the maximized profit and determine how many batches of each can size should be produced.

Answer 1

Answer:

	Large	Medium	Small	Maximum Availability
Metal (kg)/batch	9	6	5	200
Machines Time (hr)/batch	4.4	4.2	4	105
Profit/Batch	51	40	42

a. Linear Programming Model:

Decision Variables: Let L, M, and S be the no. of batches of cans produced for sizes Large, Medium, and Small respectively.

Objective Function: To maximize the total profit.

Maximize 51L + 40M + 42S

b. Constraints:

9L + 6M + 5S <= 200 (Metal Availability per batch)

4.4L + 4.2M + 4S <= 105 (Machine hrs availability per batch)

L, M, S >= 0 (non negativity constraints)

c. Solving the LP in solver:

The solver is an excel plug in which can be installed form excel options. After installation, it is available in the data segment of the excel sheet. Once installed and launched, the parameters can be added

Spreadsheet Model along with formulae used:

Adding Parameters in Solver:

blue is data

in the solver, provide cell reference of red highlighted cell in the set objective field

select max

provide orange highlighted cells reference in the changing variables cells

constraints: yellow highlighted are constraints formulae and green are the rhs values.

select the make unconstrained variables non-negative (non-negative constraint)

select the solving method as simplex LP

click solve to get the solution

Solution:

Ans:

Maximized profit = 1196.79 (rounded value)

No. of batches of each size produced:

L	M	S
19.64	0	4.643

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