Question

Formulate and solve the following LPs in Excel. Only the first two are provided for now. I will complete the assignment after I return from the conference.

1. Maggie loves desserts, but due to health concerns, she has decided that she must plan carefully. There are two desserts that she is considering: snack bars and ice cream. After reading the nutrition labels, she learns that each serving of the snack bar weighs 137 grams and contains 120 calories and 5 grams of fat. Each serving of the ice cream weighs 65 grams and contains 160 calories and 10 grams of fat. Maggie will allow herself no more than 450 calories and 25 grams of fat in her daily desserts, but because she loves desserts so much, she requires at least 120 grams of dessert per day. Also, she assigns a “taste index” to each gram of each desserts, where 0 is the lowest and 100 is the highest. She assigns a taste index of 95 to ice cream and 85 to snack bars.

Formulate and solve an LP that determines the daily dessert plan that maximizes the total taste index of her dessert.

2. For a telephone survey, a marketing research group needs to contact at least 600 wives, 480 husbands, 400 single adult males, and 440 single adult females. It costs $3 to make a daytime call and $5 to make an evening call. The following table summarizes the percentage of various respondents for each type of phone call.

Person responding	% of daytime calls	% of evening calls
Wife	30	30
Husband	10	30
Single male	10	15
Single female	10	20
None	40	5

For example, 30% of all daytime calls are answered by a wife, 15% of all evening calls are answered by a single male, and 40% of all daytime calls are not answered at all. Due to limited staff, at most 40% of all phone calls can be evening calls.

Determine how to minimize the cost of completing the survey.

3. Work problem 12.7 on page 595 in the book.
4. Work problem 12.12 on page 598 in the book.
5. Work problem 12.25 part a on page 604 in the book.

Answer 1

Let assign variable,

X for each gram of ice cream

Y for each gram of sanck bar

Max 95*X+ 85*Y

Subject to,

X+Y>=120

(120/137)*X +(160/65)*Y<=450

(5/137)*X+(10/65)*Y<=25

Here, calories and fat equation is in Fraction because given data is per pack.

Here we convert calories and fat per each gram of ice cream and snacks bar respectively.

2)

Again 1st assign variable

X- no. Of call in day time

Y-no. Of call in evening

Min . 3*X+5*Y

Subject to,

0.30X+0.30Y>=600

0.10X+0.30Y>=480

0.10X+0.15Y>=400

0.10X+0.20Y>=440

0.40X+0.05=1920

X<=0.40*1920

X<=768