Question

A farmer can grow wheat or corn. The unit profits for a bushel of each are the same. To grow wheat (W) and corn (C), the farmer requires four input factors: Capital (K), land (L), A-Fertilizer (A), and B-fertilizer (B). The production of one bushel of corn requires two units of capital and the production of one unit of wheat four units of capital. The farmer has 32 units of capital available. The production of one bushel of corn requires two units of land and the production of one unit of wheat one unit of land. The farmer has 20 units of land available. The production of one bushel of corn requires two units of A- Fertilizer, and no B-fertilizer. The farmer has 18 units A-Fertilizer available. The production of one bushel of wheat requires one unit of B fertilizer, and no A-fertilizer. The farmer has 6 units of B-Fertilizer available. The fa ner wants to maximize profits. In programming the above model into Excel, you have to fill out a spreadsheet like the one below. B A 1 2 Corn Wheat Unit Profits 3 1 Opt. Solution 1 Opt. Quant a. Constraints Corn Wheat Actual Usage Maximum Allowable Usage 7 Capital b. j. C. n. Land d. k. e. O. 9 A-Fertilizer f. I. 8 p. 10 B-Fertilizer h. m. q.

Answer 1

Let considen, us of grawing bushel and Corn:z ot wheat gaowing Ibushel = 12 profit tre Z. hawe to maximize We Wheat Corn optimal solubion profita Opt. Quant ly Unit 7, = 8 2=4 2 Mazimum Wheat Usage Constraints COrn A vailable 32 27,t 42 capital 20 221+2 2 Land 18 21 A- Fertiliz 2 zeY B- Fer tilizer Max z = x, +72 problem given to The the constraink Subject 32 27,+ 4 2 L 20 22, + 22 L 18 22 L6, solve graphically and can 7,, X2 0. We do t

are eguations The 2x,+402 = 32 20 2 71t 22 16 15 =18 2 21 2=6 13 12 |2) D 9 →저=9 7 6- F(4, 6 4 - 2 i 2 1324 s 16 17 8 7 8 (o,6)B FoY 2'x,+ 2- 20 FoY 27,t4x2 32 16 1 10 2 0 ind To Points Z=1t2 Z: X, +X2 Max A Ca,0) B CO,6) /Max Z= 12 E (8, 4) c CO,o D C9, 2) lat ID 12 E (8,4 972 -CN