Question

A brewery produced regular beer and a low carb "light beer". Steady Customers of the brewery buy 10 units of regular beer and 15 units of light beer monthly. While setting up the brewery to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular is $32,000 and the cost per unit if light beer is $50,000. Every unit of regular beer brings in $120,000 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 20 additional units of beer can be sold (a) How much of each type of beer should be made so as ti minimize total production cost (b) Suppose the minimum revenue is increased to $9,500,000.Calcualte the total production cost

Answer 1

Regular Low Carb Total

a) Units to be produced 20 22 42

(to minimize total production cost)

b) Total production costs $704,000 $1,150,000 $1,854,000

Step-by-step explanation:

a) Data and Calculations:

Regular Low Carb

Monthly customers demand 10 15

Ratio of customers demand 40% 60%

Cost per unit $32,000 $50,000

Revenue per unit 120,000 300,000

Contribution per unit $88,000 $250,000

Total required revenue = $9,000,000

With 20 additional units of beer, total units produced = 45 (25 + 20)

To minimize production costs and generate a total revenue of $9,000,000, more of the units that cost less should be produced. Units should be produced according to the following ratio:

Regular Low Carb Total

New Production and Sales units 20 22 42

Total production cost = $640,000 $1,100,000 $1,740,000

($32,000 * 20) ($50,000 * 22)

Total revenue = $2,400,000 $6,600,000 $9,000,000

($120,000 * 20) ($300,000 * 22)

To achieve a minimum revenue of $9,500,000,

New production units 22 23 45

Total production cost = $704,000 $1,150,000 $1,854,000

Total revenue = 2,640,000 6,900,000 9,540,000