Question

Field Sports Equipment Inc. (FSE) produces basketballs at its factory in Hamilton and soccer balls at its factory in Windsor. At its current annual rate of production, the cost of producing basketballs is $70,000 and the cost of producing soccer balls is $45,000. You are the manager of FSE and your team has developed a new study concerning FSE production costs. If FSE consolidates production at a single location, the annual cost of production will be $100,000.

2.1) You have concluded that if FSE consolidates production at one location, there will be important advantages in terms of economies of scope. Later, you have a meeting with the CEO of FSE who is not familiar with this important economic concept. Explain in two sentences what economies of scope means.

2.2) Compute the degree of economies of scope for FSE if it decides to consolidate production and interpret your numerical result.

2.3) A year has passed after FSE consolidated its production at a single location, and your team has estimated the cost function for FSE in equation (1), where ? the number of soccer balls produced. ?? = 2,000 + 120? (1) Compute the break-even point of production for FSE if the average market price for a soccer ball is $145. Interpret your numerical result.

2.4) What is break-even analysis? Why is it useful to estimate the break-even point? Respond with short answers.

2.5) Based on 1.3), draw both, the Total Revenue (TR) and the Total Cost (TC) curves on a diagram labelled “Figure 1”. Label properly both axes. Indicate the following on Figure 1: (a) the intersection points of each curve on both axes if applicable, (b) the break- even point, and (c) the sections of the curves where FSE obtains profits and losses.

2.6) It is the end of the year and your team is working on the sales projections for FSE soccer balls. You have estimated that the level of sales should satisfy a profit target of $500. Estimate the number of soccer balls that FSE has to sell to achieve this profit target.

2.7) Compute the values obtained for TR and TC if FSE sells the number of soccer balls satisfying its profit target. 2.8) Indicate on Figure 1 the number of soccer balls and the values obtained for the TR and TC satisfying FSE profit target.

Answer 1

let the number of soccer ball = x

and number of cork ball = y

then the production time equation would be:

3x + 4y ≤500

The number of the balls must be atleast 150

x + y ≥150

x ≥ 0

y ≥ 0

.

The objective would be

MinimumZ = 9X + 7Y

.

We can solve the same in excel and get the output as shown below

We can use slover as shown below

The output is as shown below

Thus 100 soccer balls and 50 cork balls must be produced.