Question

Problem 1. A flower shop makes three different types of flower arrangements: inside arrangements, wedding arrangements and garden arrangements. In a week, each inside arrangement requires 25 roses, 40 gerberas and 20 stephanotis, each wedding arrangement requires 50 roses, 10 gerberas and 25 stephanotis, and finally one garden arrangement requires 100 roses, 80 gerberas and 150 stephanotis. Each week the flower shop has 1000 roses, 850 gerberas and 2000 stephanotis to use. There is a commitment to make at most 10 inside arrangements and at least 5 wedding arrangements every week. Also, the number of the garden arrangements should not exceed the number of inside arrangements. If the profit is $15 for each inside arrangement made, $20 for each wedding arrangement and $30 for each garden arrangement made, how many arrangements of each type should the flower shop make so that will maximize their profit? A) Maximize 15.0+20y+30z subject to r < 10, y > 0,2 > 0, 25x+50y+100% <1000, 40x+10y+802 < 850, 20:r + 25y + 150z < 2000, < > 2; B) Maximize 15.0+20y+30z subject to r > 10, y > 5,2 > 0, 250+50y+1002 < 1000, 40.r+10y+802 < 850, 20:r + 25y + 150z < 2000, < > 2; C) Maximize 15x+20y+30z subject to r> 10, y >5, > 0, 25x+50y+100% <1000, 40.x+10y+80z < 850, 20:+ 25y + 150z <2000, 0, 3 < 10 y > 5, 2 > 0, 25x + 50y + 100% < 1000, 400 +10y + 802 < 850, 200 + 25y + 150z < 2000, < 0, 1 < 10, y > 5, 2 > 0, 25x + 50y + 100% < 1000, 40x + 10y + 80< 850, 20.1 + 25y + 150z < 2000, < > z; F) none of these.