Chocolate Delight Company $($CDC$)$ makes specialty chocolates and can produce $40$ pieces per hour. The firm estimates that the variable cost of producing chocolate is $$0\mathrm{.}35$ per piece and each piece sells for $$0\mathrm{.}60.$

Smiles For All $($SFA$)$ is a large greeting card company and it has asked CDC to produce a special flat chocolate greeting card for them and will pay $$2\mathrm{.}50$ for each chocolate card. The cost to manufacture the new card will be $$1\mathrm{.}80$ each. If this order is accepted, CDC will have to buy a new machine at a cost of $$12,000.$ The new machine will be able to produce $20$ cards per hour. SFA offers to buy $70,000$ cards. CDC has a capacity of $10,000$ machine hours available for both the new chocolate card and existing production and fixed costs of $$400,000$ for its regular production activity.

Instructions

a$)$ Assume the demand for its own chocolates is $250,000$ pieces. SFA says that the chocolate card order has to be produced in total or not at all. Should CDC accept the special order? $(5$ points$)$

b$)$ Assume the demand for its own chocolates is $300,000$ pieces. SFA says that the chocolate card order has to be produced in total or not at all. Should CDC accept the special order? Are there any other considerations that CDC should keep in mind? $(5$ points$)$

c$)$ Assume the demand for its own chocolates is $275,000$ pieces and CDC can decide to accept any quantity of the chocolate card order. Determine the mix of chocolates and cards that it should produce. $(5$ points$)$