STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of Pattern 12ft. 15ft. 30ft. Trim Loss
1 0 4 1 10 ft.
2 4 3 0 7 ft.
3 8 0 0 4 ft.
4 2 1 2 1 ft.
5 2 3 1 1 ft.
Trim loss is the leftover paper from a pattern (for example, for pattern 4, 2(12) 1 1(15) 1 2(30) 5 99 feet used results in 100 – 99 5 1 foot of trim loss). Demands this week are 5670 12-foot rolls, 1680 15-foot rolls, and 3350 30-foot rolls. Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss (leftover paper from a pattern).

6. why the aggregate supply curve slopes upward in the short run in the short run, the quantity of output that firms supply can deviate from the natural level of output if the actual price level in the economy deviates from the expected price level. several theories explain how this might happen. for example, the misperceptions theory asserts that changes in the price level can temporarily mislead firms about what is happening to their output prices. consider a soybean farmer who expects a price level of 100 in the coming year. if the actual price level turns out to be 90, soybean prices will , and if the farmer mistakenly assumes that the price of soybeans declined relative to other prices of goods and services, she will respond by the quantity of soybeans supplied. if other producers in this economy mistake changes in the price level for changes in their relative prices, the unexpected decrease in the price level causes the quantity of output supplied to the natural level of output in the short run.