Question

California​ Gardens, Inc.,​ prewashes, shreds, and distributes a variety of salad mixes in​ 2-pound bags. Doug​ Voss, Operations​ VP, is considering a new​ Hi-Speed shredder to replace the old​ machine, referred to in the shop as​ "Clunker." Hi-Speed will have a fixed cost of ​$89 comma 000 per month and a variable cost of ​$1.25 per bag. Clunker has a fixed cost of only ​$30 comma 000 per​ month, but a variable cost of ​$1.65. Selling price is ​$2.50 per bag. ​a) What is the crossover point in units​ (point of​ indifference) for the​ processes? The crossover point is nothing units. ​(Round your response to the nearest whole​ number.)

Answer 1

The crossover point in units for California Gardens, Inc. to be indifferent between using the new Hi-Speed shredder and the old Clunker is 147,500 bags. This is calculated by setting the total costs of both shredders equal to each other and solving for the quantity of bags produced.

Step-by-step explanation:

To find the crossover point in units for the processes, we set the total costs of both machines equal to each other. The total cost for each shredder consists of the fixed cost plus variable costs, which depend on the number of units produced. For the Hi-Speed shredder, the total cost is $89,000 (fixed cost) plus $1.25 per bag (variable cost). For Clunker, it's $30,000 (fixed cost) plus $1.65 per bag (variable cost).

So the equation to find the number of bags (let's call it X) at which both shredders have the same total cost is:

89,000 + 1.25X = 30,000 + 1.65X

Solving for X gives us:

X = (89,000 - 30,000) / (1.65 - 1.25)

X = 59,000 / 0.40

X = 147,500 bags

Therefore, the crossover point is 147,500 bags. At this level of production, the costs of operating either shredder would be the same.

Answer 2

131,111 units

Step-by-step explanation:

Giving the following information:

Hi-Speed will have a fixed cost of ​$89,000 per month and a variable cost of ​$1.25 per bag. Clunker has a fixed cost of only ​$30,000 per​ month, but a variable cost of ​$1.65.

Hi-Speed= 89000 + 1.25*x

Clunker= 30,000 + 1.65*x

30,000 + 1.65x = 89,000 + 1.25x

0.45x = 59,000

x= 131,111 units