Suppose you are the chief executive officer of a small pharmaceutical company that manufactures generic aspirin. You want the company to maximise its profits. You can sell as many aspirins as you make at the prevailing market price. You have only one manufacturing plant, which is a constraint. The marginal costs of production are constant Monday through Saturday. Labour costs are higher on Sundays because you have to pay penalty rates.

Now you obtain a long-term contract to manufacture a brand-name aspirin. The costs of making the generic aspirin or the brand-name aspirin are identical. In fact, there is no significant cost or time involved in switching from the manufacture of one to the other. You will make much larger profits from the brand-name aspirin, but demand is limited. One day of manufacturing each week will permit you to fulfil the contract. You can manufacture both the brand-name and the generic aspirin. Compared with the situation before you obtained the contract, your profits will be much higher if you now begin to manufacture on Sundays – even if you have to pay penalty rates.

Generic aspirin. Each day, you can make 1,000 cases of generic aspirin. You can sell as many as you make, for the market price of $20 per case. Every week you have fixed costs of $10,000 (general utilities, rates and insurance). No matter how many cases you manufacture, the cost of materials and supplies is $4 per case; the cost of labour is $10 per case, except on Sundays, when it is $20 per case.

Brand-name aspirin. Your order for the brand-name aspirin requires that you manufacture 1,000 cases per week, which you can sell for $60 per case. The cost of for brand-name aspirin is identical to the cost of the generic aspirin.

A) Find the optimal production schedules with and without the new order for the brand-name aspirin.

B) Find the break-even volumes when producing brand-name aspirin first, and when producing the generic aspirin first.