The Kazak Film company needs to cut 15 long rolls and 10 short rolls of film from stock pieces. Each stock piece can be cut in one of two patterns. The first produces 5 long and 2 short rolls; the second yields 3 long and 5 short. Once any part of a piece of stock is cut, anything that remains is scrap. Also, neither pattern should be used more than 4 times because the jig used to cut it will become too inaccurate. Kazak wants to find the allowable combination of patterns that will minimize the number of stock pieces required.

mark, a civil engineer, entered into a contract with david. as per the contract, mark agreed to design and build a house for david for a specified fee. mark provided david with an estimation of the total cost and the contract was mutually agreed upon. however, during construction, when mark increased the price due to a miscalculation on his part, david refused to pay the amount. this scenario is an example of a mistake.

Tri fecta, a partnership, had revenues of $369,000 in its first year of operations. the partnership has not collected on $45,000 of its sales and still owes $39,500 on $155,000 of merchandise it purchased. there was no inventory on hand at the end of the year. the partnership paid $27,000 in salaries. the partners invested $48,000 in the business and $23,000 was borrowed on a five-year note. the partnership paid $2,070 in interest that was the amount owed for the year and paid $9,500 for a two-year insurance policy on the first day of business. compute net income for the first year for tri fecta.

Power plants that rely on coal increase the amount of sulfur dioxide that dissolves into the air, eventually increasing the acidity of precipitation. the higher acidity of rain and snow can damage forests by making it more difficult for plants to absorb minerals from the soil. the equations below provide information about the market demand and supply of electricity. there is a constant marginal external cost of $25 per unit of electricity.d: qd= 200 – 2ps: qs=p – 10what quantity of electricity satisfies allocative efficiency in this market? a. 60b. 70c. 50d. 43.3