A food is manufactured by refining raw oils and blending them together. The raw oils come in two categories; Vegetable oils (VEG1 and VEG2), and Non-vegetable oils (OIL1, OIL2, and OIL3). Vegetable oils and non-vegetable oils require different production lines for refining. In any month it is not possible to refine more than 200 tons of vegetable and no more than 250 tons of non-vegetable oils. There is no loss of weights in the refining process and the cost of refining may be ignored. There is a technical restriction of hardness in the final product. In the units in which hardness is measured this must lie between 3 and 6. It is assumed that hardness blends linearly. The costs (per ton) and hardness of the raw oils are: VEG1 VEG2 OIL1 OIL2 OIL3 Cost ($) 110 120 130 110 115 Hardness 8.8 6.1 2.0 4.2 5.0 The final product sells for $150 per ton. Formulate this problem as a linear programming model to determine how much to make of each product so as to maximize their net profit.

What is the most important type of decision that the financial manager makes?

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

Suppose a holiday inn hotel has annual fixed costs applicable to its rooms of $1.2 million for its 300-room hotel, average daily room rents of $50, and average variable costs of $10 for each room rented. it operates 365 days per year. the amount of operating income on rooms, assuming an occupancy* rate of 80% for the year, that will be generated for the entire year is *occupancy = % of rooms rented