Reconsider the Special Products Company problem pre-sented 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

Supply

= 30 shipments 50 shipments

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 differ-ence in profit between the make and buy options in terms of the number of grandfather clocks to pro-duce 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 mathemati-cal 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?