Question

AVP of a manufacturing firm that produces two products has to decide (1) How much capacity to build? (2) Whether to invest in dedicated or flexible resources, or a portfolio consisting of both dedicated and flexible systems. The VP received the following forecasting for the demand of each product. Year 1–2 Year 3–6 Volume Volume Probability Product A 500,000 200,000 0.7 600,000 0.3 Product B 200,000 200,000 0.3 600,000 0.7 A dedicated line can produce 300,000 annually and its cost is $30 million. Flexible systems are supplied at chunks; each has an annual production capacity of 50,000 units and costs $7 million. The revenues from each product sold are $40. (a) Calculate the optimal capacity—type and quantity. (b) What is the optimal solution if the cost of a dedicated line that can produce 200,000 annually is $15 million? (c) What is the optimal solution if the cost of a dedicated line that can produce 300,000 annually is $40 million?

Answer 1

Demand for each variety = 100 units

Revenue from each place = $10

Cost per variety = $500

Fixed cost = $750

a) We offer all the variety then the cost

total cost =fixed cost+(4*cost per variety)

=$750+(4*500)

=$2,750

calculation of income= no. of units *revenue*4

=100*10*4

=$4,000

b) remove six inches  variety then cost

Total cost = $750+(3*500)

  =$2,250

calculations of income =(100*10*3)+(60*10)

=$3,600

Customers who wants six inches will go to the 8 inches. The rest of the 40 customers will not be able to buy six inches s not available from observation we can smartly choose a combination of where most of the customers here option to buy a and we offer the minimum variety.

c) let us remove six and ten inches then the cost

Total cost = $750+50*2

=$1,750

calculation of the income=((60*10)+(100*10)+(40*10)+(60*10))+(100*10)

=$2,000+$1,600

=$3,600

percentage of profits in case (a)

=4,000-2750/2,750*100

=45.45%

percentage of profits in case(b)

=3,600-2,250/2,250*100

=60%

percentage of profit in case(c)

=3,600-1,750/1,750*100

=105.7%

The maximum profit is earned by offering 8 and 12 inches.