plz help Ill rate Problem 57 whether to purchese the motors

plz help I\'ll rate

Problem 5-7 whether to purchese the motors for the A firm plans to begin production of a new small appliance. The manager must decide appliance from a vendor at S -house. Either o ble cost of $5 per unit, and the other would have an annual fixed cost of processes could be used for in-house production; one 7 each or to produce them in would have an annual fixed cost of $160.000 and a variab $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of (Round your answer to the neerest whole number.) the alternatives would be best For annual volume ess than (Ci to salecys best For larger quenties, best to pro is best. For larger quantities, best to produce in house at $ For annual volume less than per unit **

Solution

Let the corresponding threshold volume = N

At volume N :

Total cost of purchasing from a vendor = $ 7.N

Total cost of making it in house through first process , $ = 160,000 + 5.N

Total cost of making it in house through second process , $ = 190,000 +4.N

Applicable volume for buying it from outside vendor :

One will buy from outside vendor if,

Total cost of purchasing from vendor < Total cost of making it in house through first process,

As well as,

Total cost of purchasing from vendor < Total cost of making it in house through second process

Therefore ,

7N < 160,000 + 5.N

Or, 2.N < 160,000

Or, N < 80,000

As well as ,

7.N < 190,000 + 4.N

Or, 3.N < 190,000

Or, N < 190,000/3

Or, N < 63333.33

Taking into account both constraints N < 80,000 as well as N < 63333.33 together, the relevant answer would be

N < 63333.33

Applicable volume for making it in house through first process :

One will make it in house through first process when:

Cost of making it in house through first process < Cost of buying it from outside vendor

As well as

Cost of making it in house through first process < Cost of making it through second process

Therefore,

160,000 + 5.N < 7.N

Or, , 2N> 160,000

Or, N > 80,000

As well as ,

160,000 + 5.N < 190,000+ 4.N

Or, N < 30,000

It is however not possible to have a value of N which satisfies N > 80,000 as well as N > 30,000.

Applicable volume for making it in house through second process:

Cost of making it in house through second process < Cost of buying from outside vendor

As well as

Cost of making it in house through second process < Cost of making it in house through first process

190,000 + 4.N < 7.N

Or, 3.N > 190,000

Or, N > 63333.33

As well as ,

190,000 + 4.N < 160,000 + 5.N

Or, N > 30,000

Taking into account both constraints together i.e N > 30,000 as well as N > 63333.33,

It should be N > 63333.33

IT THUS CAN BE SUMMARIZED THAT :

FOR VOLUME LESS THAN 63,334 IT IS BEST TO BUY FROM OUTSIDE VENDOR. FOR LARGER QUANTITIES IT IS BEST TO PRODUCE IN HOUSE THROUGH SECOND PROCESS ( i.e $4 / UNIT )

FOR ANNNUAL VOLUME LESS THAN 63334 PURCHASING THE MOTORS FROM A VENDOR IS BEST, FOR LARGER QUANTITIES , BEST TO PRODUCE IN HOUSE AT $4 PER UNIT

FOR ANNNUAL VOLUME LESS THAN 63334 PURCHASING THE MOTORS FROM A VENDOR IS BEST, FOR LARGER QUANTITIES , BEST TO PRODUCE IN HOUSE AT $4 PER UNIT