Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)

z (min)  =  2079

L = 26     D =  39.6    S  =  16.5

Step-by-step explanation:

L  numbers of hours assigned to Lisa

D numbers of hours assigned to David

S numbers of hours assigned to Sara

Objective Function to minimize:

z = 30*L  +  25*D  +  18*S

Constraints:

Total time available

L  +  D  +  S  ≤ 110

Lisa experience

L  ≥  0.4 *  ( L + D )  then    L ≥ 0.4*L  +  0.4*D

0.6*L - 0.4*D ≥ 0

To provide designing experience to Sara

S ≥ 0.15*110        then     S ≥ 16.5

Time for Sara

S  ≤ 0.25 * ( L + D )     S ≤ 0.25*L  +  0.25*D   or    -0.25*L - 0.25*D + S ≤0

Availability of Lisa

L ≤ 50

The Model is:

z = 30*L  +  25*D  +  18*S  to minimize

Subject to:

L  +  D  +  S  ≤ 110

0.6*L - 0.4*D ≥ 0

S ≥  16.5

-0.25*L - 0.25*D + S ≤0

L ≤ 50

L ≥   0  ;   D  ≥  0  , S  ≥  0

After  6  iterations  optimal ( minimum ) solution is:

z (min)  =  2079

L = 26     D =  39.6    S  =  16.5

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.