Answer:
a) Oven A = 1,667; Oven B = 2,353 pizzas.
b) Oven A
c) Oven A
d) 13,334 pizzas
Explanation:
Since nothing was mentioned regarding her time availability, the capacity of each oven will not be taken into account.
The income equation for ovens A and B, respectively, are:
![A=(14-2)x-20,000\\B=(14-1.25)x-30,000](https://tex.z-dn.net/?f=A%3D%2814-2%29x-20%2C000%5C%5CB%3D%2814-1.25%29x-30%2C000)
Where 'x' is the number of pizzas sold.
a) The break-even occurs when income is zero:
![A=0=(14-2)x-20,000\\x_A=1,666.66\\B=(14-1.25)x-30,000\\x_B=2,352.94](https://tex.z-dn.net/?f=A%3D0%3D%2814-2%29x-20%2C000%5C%5Cx_A%3D1%2C666.66%5C%5CB%3D%2814-1.25%29x-30%2C000%5C%5Cx_B%3D2%2C352.94)
Rounding up to the next whole pizza, the break-even for oven A is 1,667 pizzas and for oven B it is 2,353 pizzas.
b) For x = 9,000:
![A=(14-2)*9,000-20,000\\A=\$88,000\\B=(14-1.25)*9,000-30,000\\B=\$84,750](https://tex.z-dn.net/?f=A%3D%2814-2%29%2A9%2C000-20%2C000%5C%5CA%3D%5C%2488%2C000%5C%5CB%3D%2814-1.25%29%2A9%2C000-30%2C000%5C%5CB%3D%5C%2484%2C750)
Income is greater with oven A, so Janelle should use oven A.
c) For x = 12,000
![A=(14-2)*12,000-20,000\\A=\$124,000\\B=(14-1.25)*12,000-30,000\\B=\$123,000](https://tex.z-dn.net/?f=A%3D%2814-2%29%2A12%2C000-20%2C000%5C%5CA%3D%5C%24124%2C000%5C%5CB%3D%2814-1.25%29%2A12%2C000-30%2C000%5C%5CB%3D%5C%24123%2C000)
Income is greater with oven A, so Janelle should use oven A.
d) She should switch ovens at the value for 'x' that causes B to be greater than A:
![A](https://tex.z-dn.net/?f=A%3CB%5C%5C%2814-2%29%2Ax-20%2C000%3C%2814-1.25%29%2Ax-30%2C000%5C%5C10%2C000%3C0.75x%5C%5Cx%3E13%2C333.33)
Rounding up to the next whole pizza, she should switch ovens at a volume of 13,334 pizzas.