Customers buy 11 units of regular beer and 14 units of light beer monthly. The b

Question

Customers buy 11 units of regular beer and

14 units of light beer monthly. The brewery decides to produce extra beer, beyond that needed to satisfy the customers. The cost per unit of regular beer is

$35,000 and the cost per unit of light beer is $45,000. Every unit of regular beer brings in $150,000 in revenue, while every unit of light beer brings in

$300,000 in revenue. The brewery wants at least $9,000,000 in revenue. At least 22 additional units of beer can be sold.

How much of each type of beer should be made so as to minimize total production costs? Let

y 1 represent units of regular beer and y2 represent units of light beer. Find the objectivefunction, w, used to minimize production costs.

Explanation / Answer

Let say there are y1 units of regular beer and y2 units of light beer.

The objective function of total cost

Total cost = TC = w = 35000 y1 + 45000 y2

Constaint to :

Revenue Constraint

150000 y1 + 300000 y2 >= 90,00,000

y1 + 2y2 >= 60 .....(i)

y1 >= 11 ..(ii)

y2 >= 14 ...(iii)

y1 + y2 >= 11 + 14 + 22

y1 + y2 >= 47 ...(iV)

By using excel solver

Units of regular Beer y1 = 33

Units of light beer y2 = 14

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