Use the case study problem given on the next page $($or see page $204$ of textbook$)$ to answer the following questions:

a$.$ Formulate a linear programming model $($identify and define decision variables, objective function and

constraints$)$ that can be used to determine the advertising budget allocation for the Flamingo Grill in order.

to maximize the total exposure rating. $(20$ points$)$ Decision Variables: $-(()/())/($Y$\_(\backslash$Delta $)$t$)$ : Number of TV adds to

buy. $(-)/(()/())($Y$\_(\backslash$Delta $)($r$)/(()/()))$ : Number of radio ads to buy. $-(()/())/($Y$\_(\backslash$Delta $)($n$)/(()/()))$ : Number of newspaper articles to buy. Objective

Function: Maximize $($Z$=90$x$\_($t$)+70$x$\_($r$)+35($x$\_($n$))/(()/()))$

Constraints: Y$\_(\backslash$Delta $)$t$+$Y$\_(\backslash$Delta $)$r$+$Y$\_(\backslash$Delta $)$n$()/(-)>1($Take out at least one add per source$)$

Budget Constraints $-$ Budget limit of $$279,000$

$+-10,000$Y$\_($t$)+3000$Y$\_($r$)+1000($Y$\_($n$))/(()/())$leq$\_(2)279,000$

Exposure Constraints $-$ Total exposure rating must be maximized.

$+-(90$Y$\_($t$)+70$Y$\_($r$)+35($Y$\_($n$))/(()/())$geq$100,(000)/(()/()))$

Balance between media $-$ They need to use twice as many radio adds vs$.$ TV commercials.

b$.$ Use Solver in Microsoft Excel to solve the model that you developed in part $($a$).$ Give the values of each

decision variable and the objective function. Also indicate the total number of new customers reached. You

MUST attach a copy of the solution report. $(10$ points$)$

$**$See Excel spreadsheet.

c$.$ How would the total exposure change if an additional $$10,000$ were added to the advertising budget?

Explain. $(5$ points$)$ The total exposure would increase due to adding to the $279,000$ total budget for

advertising.

d$.$ Comment on the ranges for the objective function coefficients. What do the ranges indicate about how

sensitive the recommended solution is to HJ$\text{'}$s exposhre rating coefficients? Explain. $(5$ points$)$

The ranges are a good starting point to indicate that the exp rating is a solid point on getting each of the

broadcasting examples $($tv$,$ newspaper and radio$)$ to the general public while keeping tv commercials at the top of

the list.

e$.$ After reviewing HJ$\text{'}$s recommendation, the Flamingo's management team asked how the optimal solution

would change if the objective of the advertising campaign was to maximize the number of potential new

customers reached. Use Solver in Microsoft Excel to solve this new model that you developed in part $($e$).$

Give the values of each decision variable and the objective function. Also indicate the total exposure

rating. You MUST attach a copy of the solution report. $(5$ points$)$

f$.$ Compare the optimal solutions from part $($b$)$ and part $($e$).$ Which objective function is a better indicator of

advertising effectiveness? Please comment $(5$ points$)$ Part B is the better indicator of advertising due to the

effectiveness of reach potential customers.

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods

from around the world. Two of the store's leading products use the Romans Food Market

name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of

Brazilian Natural and Colombian Mild coffee beans, which are purchased from a dis$-$

tributor located in New York City. Because Romans purchases large quantities, the coffee

beans may be purchased on an as$-$needed basis for a price $10\%$ higher than the market

price the distributor pays for the beans. The current market price is $$0\mathrm{.}47$ per pound for

Brazilian Natural and $$0\mathrm{.}62$ per pound for Colombian Mild. The compositions of each

coffee blend are as follows:

Romans sells the Regular blend for $$3\mathrm{.}60$ per pound and the DeCaf blend for $$4\mathrm{.}40$ per

pound. Romans would like to place an order for the Brazilian and Colombian coffee beans

that will enable the production of $1000$ pounds of Romans Regular coffee and $500$ pounds

of Romans DeCaf coffee. The production cost is $$0\mathrm{.}80$ per pound for the Regular blend.

Because of the extra steps required to produce DeCaf, the production cost for the DeCaf

blend is $$1\mathrm{.}05$ per pound. Packaging costs for both products are $$0\mathrm{.}25$ per pound.

Part a $($worth $60$ pts$)$: Formulate a linear programming model $($identify and define decision

variables, objective function and constraints$)$ that can be used to determine the amount $($in

pounds$)$ of Brazilian Natural and Colombian Mild that will maximize the total contribution

to profit. For "Part a $"$ you do NOT need to solve this problem using Excel, you just need to

do the LP formulation in the standard mathematical format.

Decision Variables:

BB$=$ pounds of Brazilian beans purchased to produce Regular blend

BD$=$ pounds of Brazilian beans purchased to produce Decaf blend

CB$=$ pounds of Columbian beans purchased to produce Regular blend

I need help with PROBLEMS: A$-$F$.$