Engineering economy analysis"questions found in everyday's general analysis"

Problem 1

  A firm is planning to manufacture  a new product . As  the selling price  is increased , the quantity  that can be sold decreases. Numerically the sales department estimates :

P= $350+ 0.2Q 

Where P= Selling price per unit 

            Q= Quantity sold per year 

On the other hand management estimates that the average  rate cost  of  manufacturing and selling the product will decrease as the quantity  sold increases . They estimate

C= $ 40Q+$20000 

Where C= cost to produce and sell Q per year . The firm's management wish to maximize profit . What quantity should the decision makers plan to produce  and sell each  year  and what profit will be earned  ? 

   

Solution :

 Profit = Income – Cost

  = PQ– C

where: PQ = 350Q − 0.20Q^2

 C = 40Q + 20,000

  

 Profit = 310Q - 0.20Q^2

  - 20,000

 d(Profit)/dQ = 310 − 0.40Q = 0

 Solve for Q:

 Q = 310/0.4 = 775 units/year

  

 d2

 (Profit)/dQ2

 = –0.40

 The negative sign indicates that profit is maximum at Q equals 775 units/year.

 Answer: Q = 775 units/year

Problem 2

A manufacturer is considering replacing a production machine tool. The new machine would cost $37000, have a life of 4 years, have no salvage value, and save the fund $5000 per year in direct labor costs and $2000 per year indirect labor costs. The existing machine tool was purchased 4 years ago at a cost of $40000. It will last 4 more years and have no salvage value at the end of that time. It could be sold now for $10000 cash. Assume money is worth 8%, and that the difference in taxes, insurance, and so forth, for the two alternatives is negligible. Determine whether or not the new machine should be purchased.

 Solution:

New Machine

 EUAC = $37,000 (A/P, 8%, 4) − $5000 − $2000

 = $37,000 (0.3019) − $7000

 = $4170

 Existing Machine

 EUAC = $10,000 (A/P, 8%, 4)

 = $10,000 (0.3019)

 = $3019

 The new machine should not be purchased

Problem V

2-4   Venus Robotics can produce 23,000 robots a year on its daytime shift. The fixed manufacturing costs per year are $2 million and the total labor cost is $9,109,000. To increase its production to 46,000 robots per year, Venus is considering adding a second shift. The unit labor cost for the second shift would be 25% higher than the day shift, but the total fixed manufacturing costs would increase only to $2.4 million from $2 million.

Solution 

V

 Unit Manufacturing Cost

(a) Daytime Shift = ($2,000,000 + $9,109,000)/23,000

 = $483/unit

 (b) Two Shifts = [($2,400,000 + (1 + 1.25) ($9,109,000)]/46,000

 = $497.72/unit 

Problem 3 

A firm purchased some equipment at a very favorable price of $30,000. The equipment resulted in an annual net saving of $1000 per year during the 8 years it was used. At the end of 8 years, the equipment was sold for $40,000. Assuming interest at 8%, did the equipment purchase prove to be desirable?

Solution: 

Favorable Price = $30000 Annual Saving = $1000 Time Period = 8 Years Equipment Value = $40000 Interest Rate = 8% Present Value of Equipment (Use) = Annual Saving*((1-1/(1+r)^n)/r) + Equipment Value/(1+r)^n =…

0*((1-1/(1+8%)^8)/8%) + $40000/(1+8%)^8 = $27357.39 Saving value is less than favorable price. Therefore, the equipment purchase is not desirable.