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Janelle Heinke, the owner of Ha�Peppas!, is considering a new oven in which to bake the firm�s signature dish, vegetarian pizza. Oven type A can handle 20 pizzas an hour. The fixed costs associated with oven A are $20,000 and the variable costs are $2.00 per pizza. Oven B is larger and can handle 40 pizzas an hour. The fixed costs associated with oven B are $30,000 and the variable costs are $1.25 per pizza. The pizzas sell for $14 each.

a) What is the break-even point for each oven?

b) If the owner expects to sell 9,000 pizzas, which oven should she purchase?

c) If the owner expects to sell 12,000 pizzas, which oven should she purchase?

d) At what volume should Janelle switch ovens?

Respuesta :

ridxee

Answer:

a) A = 1667 and B = 2353

b) Oven A

c) Oven A

d) Below 13,333 pizza: Oven A

Above 13,334 pizza: Oven B

Explanation:

We have the following data:

                             Oven A:                             Oven B:

Capacity                 20 p/hr                              40p/hr

Fixed Cost            $20,000                            $30,000

Variable Cost        $2.00/p                             $1.25/p

Selling Price: $14

a) Break-even point  →   Cost = Revenue

([tex]x[/tex] refers to the number of pizza sold)

Oven A:

20000 + 2[tex]x[/tex] = 14[tex]x[/tex]

20000 = 14[tex]x[/tex] - 2[tex]x[/tex]

[tex]x[/tex] = 20000/ 12

[tex]x[/tex] = 1666.67 ≈ 1667 pizza

Oven B:

30000 + 1.25[tex]x[/tex] = 14[tex]x[/tex]

30000 = 14[tex]x[/tex] - 1.25[tex]x[/tex]

[tex]x[/tex] = 30000/ 12.75

[tex]x[/tex] = 2352.9 ≈ 2353 pizza

b) Comparing both oven for 9,000 pizza

Profit = Selling Price - Cost Price

Oven A:

Profit = (9000 x 14) - (20,000 +  2 x 9000)

Profit = 126000 - 38000

Profit = 88000

Oven B:

Profit = (9000 x 14) - (30,000 +  1.25 x 9000)

Profit = 126000 - 41250

Profit = 84750

Oven A is more profitable.

c)

Oven A:

Profit = (12000 x 14) - (20,000 +  2 x 12000)

Profit = 168000 - 44000

Profit = 124000

Oven B:

Profit = (12000 x 14) - (30,000 +  1.25 x 12000)

Profit = 168000 - 45000

Profit = 123000

Oven A is more profitable.

d) Using the equation formed in a):

20,000 - 12[tex]x[/tex] < 30,000 - 12.75[tex]x[/tex]

12.75[tex]x[/tex] - 12[tex]x[/tex] < 30000 - 20000

0.75[tex]x[/tex] < 10000

[tex]x[/tex] < 10000/0.75

[tex]x[/tex] < 13333.3

Hence, if the production is below 13,333 Oven A is beneficial.

For production of 13,334 and above, Oven B is beneficial.

Answer:

a.       Find the break even points in units for each oven.

Breakeven for type A pizza x =  = 1,666.6 units of pizza need to be sold in order to obtain breakeven for Type A

Breakeven for type B pizza x =  = 2,352.9 units of pizza need to be sold in order to obtain breakeven for Type B

b.      If the owner expects to sell 9000 pizzas, which oven should she purchase?

Type B: because the profit will be twice what will be obtainable from type A considering the fact that it produces pizza at the ration of TypeB:TypeA, 40:20 or 2:1

Profit for type a = 9000/20 x 14 = 6,300 – 1,666,6units ($23, 3332) = 4366.4 units

Profit for type B = 10,247.1 units of pizza - which makes it justifiable

Explanation:

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