Question

lable Alignment Number 32 A B C F F G K L M 7. Billy D. is a manager for musical groups. Billy is working information about two different products that can be used for printing. The box with T-shirts (T) is less expensive to buy and costs on marketing material and has been presented with the following $15.00. The box of caps costs $22.00. Billy's boss asks him how many boxes should they buy of each product to MINIMIZE the costs, subject to the following constraints such as hours: (3 points each) 2 MIN 1ST 22C 3 s.t. 8T 4 4C + 200 2T 5 7C + 180 6 10T 150 7 6C 120 T,C 10 b. Use a graph to show each constraint and the feasible region, 11 C. Identify the optimal solution point on your graph. 12 d. How many boxes of T-shirts should they purchase to minimize the cost & how much will cost? 13 14 e. How many boxes of caps should they purchase to minimize the cost & how much will cost? 15 16 f. What is the optimal objective value of the objective function (dollar value)? 17 AL V AL AL AL Can yau Show tho Calculatans to each answeie piesle legle

Answer 1

The problem is L P Z = 5 T 22 C Subject to 4-C > 200 2T O T C 120 Т, с > 0 To raw cons:lraint on graph c repreents Lot T represents thie i -axis and graph. 2 D the y-axis on a 4 C 20 D Constraunt : 8Tt T = 0 when T= 25 T axis and yaxis are, 1ntersection points on 0, 25 and 2 T 7 C 180 Constraunt 2 : 25.7 C = when T o (0,40), (25-71,0) axis ano Internection DOints oh IO T constraint 3: рatallel to y. axis constraint 4 6 с parallal to - qxis 2 0 CS Scanned with CamScanner

50 45 40 3 S 25 A 2 T t7C S l8o 20 0 A0 T 7D B0 CS Scained with CanScanner Id T710 8Tt 47 10d -6

Thn extTLms poinis mamad A, B, C optimum olution The ono of this pdint 1awe function valuo at lie at wiu check obiect the eath point At poini A 100 2T 7 Lhes ISO Inter ecton poini nafes 15 T 1Sa/a 22C 5 T 1S X IS4 4 875 point B A1 8T 4 C 200 Lines 10 す nterAect ion poini 15 て= 20 2 2 c S T 22 x 20 665 cS Scanned with CamScanner

A point C 180 2 T Lines 6 C 120 Internecton point 20 22 C 15 T 22 X 20 7 40 point B Henco optimym Poir is minimum 2 in whu wi be quined e) wil huquired be 20 665 CS Sned min with CamScanner