Question

a-d

2. A company man ufactu ring fine glass accessories produces color glass vases with a flower pattem. Each vase is produced from liquid glass by an artist glass-blower and then set in a storage room to cool to the room temperature. The vases are made in two sizes-large and smal-but since the production processes are nearly identical, the two types of vases share the same resources. Each vase, irrespective of its size, takes 20 minutes of the artist's work. The artist works 40 hours each week. A small and a large vase require 10 az. and 20 oz of colored glass, respectively. A total of 1,600 oz. of colored glass is available per week. In addition, a small glass oCcupies 2 units of storage space, whereas a large vase occupies 3 units of storage space. The total available storage is 260 units. A small vase contributes $10 to earnings and a large vase contributes $12 to earnings. The company would like to maximize its con tri bution to earnings. Write the objective function of this problem according to the parameters above in terms of two decision variables S (small) and L (large). a (0.5 point) b. Write each of the constraint functions. (0.5 point each) Graph the optimization model: plot and label each constraints and shade the feasible region. (4 points) C. d. Solve for the optimal product mix. What values of the decision variab les retum the maximum contribution to earnings? What is the maximum contribution to earnings? (4 points)

Answer 1

Page Date Del X,ino. af somall Vases Xi RO o laye al X Con small ases Cantaibutes& 10 laaa cantaibuter R.$12 to the tatal eazning Qurk abiective is to maximize talal eaa ning Obrecdive fnnclian id max. 2- 10X,t12 Xa giuen in belay table Total 9400 1600 960 bThe availahle esouxcer Small Aalisl lime Imin) Calouaed glaas Telage Areis 20 20 20 hoanga Stace 2 Canslaaints 20X, t 20X, 2400 10 Xt 20X 1600 -() (2) (3) Gxaph of oplimizatian madel is 200 960 60 49.0 (2) 0 20 bo 6O R0 100

feasible egion aboe Aaph te the In of feasible aegion has ca azdi'atas O(0.0) CE(00,20) and each potht A= (0.80) 120 0) 40100) paint The ualues of objeadida function ad this is 10 X0t12x80 400 720 1000 +240 1200 120 1240 1ox40t 12x 60 1O X 100 t 12 x 20 10X120 t 12 xO Since maximizatian objediie function it af Hence optimum aalue of paint Laser and 20 1240 ndhich is Camcaponding to &m 100 Inage and aximum the maximumContaibutlion contaibution is $1240