Reconsider the Special Products Company problem presented in Section 1.2. Although the company is well qualified to do most of the work in producing the iWatch, it currently lacks much expertise in one key area, namely, developing and producing a miniature camera to be embedded into the iWatch. Therefore, management now is considering contracting out this part of the job to another company that has this expertise. If this were done, the Special Products Company would reduce its research-and-development cost to $5 million, as well as reduce its marginal production cost to $750. However, the Special Products Company also
would pay this other company $500 for each miniature camera and so would incur a total marginal cost of $1,250 (including its payment to the other company) while still obtaining revenue of $2,000 for each watch produced and sold. However, if the
company does all the production itself, all the data presented in Section 1.2 still apply. After obtaining an analysis of the sales potential, management believes that 30,000 watches can be sold. Management now wants to determine whether the make option (do all the development and production internally) or the buy option (contract out the development and production of the
miniature cameras) is better.
a. Use a spreadsheet to display and analyze the buy option. Show the relevant data and financial output, including the total profit that would be obtained by
producing and selling 30,000 watches.
b. Figure 1.3 shows the analysis for the make option. Compare these results with those from part a to determine which option (make or buy) appears to be better.
c. Another way to compare these two options is to find a break-even point for the production and sales volume, below which the buy option is better and
above which the make option is better. Begin this process by developing an expression for the difference in profit between the make and buy options in
terms of the number of grandfather clocks to produce for sale. Thus, this expression should give the incremental profit from choosing the make option
rather than the buy option, where this incremental
profit is 0 if 0 watches are produced but otherwise
is negative below the break-even point and positive
above the break-even point. Using this expression as
the objective function, state the overall mathematical model (including constraints) for the problem of determining whether to choose the make option
and, if so, how many units of the LCD display (one
per watch) to produce.
d. Use a graphical procedure to find the break-even
point described in part c.
e. Use an algebraic procedure to find the break-even
point described in part c.
f. Use a spreadsheet model to find the break-even
point described in part c. What is the conclusion
about what the company should do?