Suppose that a lumberyard has a supply of 10-ft boards, which are cut into 3-ft, 4-ft, and 5-ft boards according to customer demand. The 10-ft boards can be cut into several sensible patterns. each in such a way that there the leftover material is less than 3-ft. The lumberyard just received an order for 90 3-ft boards, 60 4-ft boards. and 60 5-ft boards.

a. Determine all sensible patterns the lumberyard may use to cut the 10-ft boards.
b. The lumberyard would like to use as few 10-ft boards as possible in meeting the demand. Write out a mathematical formulation for the problem as an integer linear program ILP), and setup/solve this problem using Microsoft Excel solver. What is the optimal number of each pattern, and what is the minimum number of boards to cut?

Which of the following statements is true about financial planning

Find the zeros of the polynomial 5 x square + 12 x + 7 by factorization method and verify the relation between zeros and coefficient of the polynomials

Greenway industries is a major multinational conglomerate. its business units compete in a range of industries, including home appliances, pharmaceuticals, commercial real estate, and plastics manufacturing. although its largest business unit, which produces kitchen appliances, is among the most profitable in the industry, it generates only 35 percent of the company's revenues. which of the following is most likely true of greenway's stock price? a. it is valued at less than the sum of its individual business units. b. it is valued at greater than the sum of individual business units. c. it is valued at the exact sum of individual business units. d. it is consistently lower than the industry average.it is valued at greater than the sum of individual business units.