Problem 01: Model the problem as a liner problem that maximize the total profit
ID: 396906 • Letter: P
Question
Problem 01: Model the problem as a liner problem that maximize the total profit A company that operates 10 hours a day manufactures two products on three sequential processes The following table summarizes the data of the problem: Minutes per unit Product Process Prcess Process 3 Unit profit 10 $2 $3 10 Problem 02: Model the problem as a liner problem that maximize the total profit ChemLabs uses raw materials Iand II to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials / and II are 150 and 145 units, respectively One unit of solution A consumes 5 unit of raw material and.6 unit of raw material II and one unit of solution B uses 5 unit of raw material Iand .4 unit of raw material II. The profits per unit of solutions A and B are $8 and $10, respectively. The daily demand for solution A lies between 30 and 150 units and that for solution B between 40 and 200 units Problem 03: Model the problem as a liner problem that maximize the total profit In the Ma-and-Pa grocery store, shelf space is limited and must be used effectively to increase profit.Two cereal items, Grano and Wheatie, compete for a total shelf space of 60 ft2. A box of Grano occupies 2 ft and a box of Wheatie needs 4 ft2.The maximum daily demands of Grano and Wheatie are 200 and 120 boxes, respectively. A box of Grano nets $1.00 in profit and a box of Wheatie $1.35. Problem 04 Investor Doe has $10,000 to invest in four projects The following table gives the cash flow for the four investments Cash flow ($1000) at the start of Year 2 Year 4 1.80 1.50 1.90 1.80 ProjectYear I Year 3 Year S 1.20 130 0.80 0.95 0.60 1.00 0.00 1.00 0.60 The information in the table can be interpreted as follows: For project 1,$1.00 invested at the start of year 1 will yield S.50 at the start of year 2, $.30 at the start of year 3, $1.80 at the start of year 4, and $1.20 at the start of year 5.The remaining entries can be interpreted similarly. The entry 0.00 indicates that no transaction is taking place. Doe has the additional option of investing in a bank account that earns 6.5% annually. All funds accumulated at the end of 1 year can be reinvested in the following year. Formulate the problem as a linear program to determine the optimal allocation of funds to investmentExplanation / Answer
Problem 01:
Decision Variables:
X1 = units of product 1 to produce
X2 = units of product 2 to produce
Objective Function:
Objective is to maximizes the profit of production mix.
Maximize Z = $2X1 + $3X2
Subject To:
Available time per day for each process = 10 hours = 10 x 60 = 600 minutes per day
Process 1 time available and required: 10X1 + 5X2 <= 600
Process 2 time available and required: 6X1 + 20X2 <= 600
Process 3 time available and required: 8X1 + 10X2 <= 600
Non-negativity constraint: X1, X2 >= 0
Problem 02:
Decision Variables:
A = units of solution A
B = units of solution B
Objective function:
Objective is to maximizes the profit of production mix. Profits per unit of solutions A and B are $8 and $10. The profit function is as follows:
Max Z = 48A + $10B
Subject To:
Raw materials I required and available: Solution A and B requires 0.5 and 0.5 units of raw material I. 150 units of raw material I is available.
0.5A + 0.5B <= 150
Raw materials II required and available: Solution A and B requires 0.6 and 0.4 units of raw material II. 145 units of raw material II is available.
0.6A + 0.4B <= 145
Daily demand of solution A lies between 30 and 150 units
Minimum requirement of A: A >= 30
Maximum requirement of A: A <= 150
Daily demand of solution B lies between 40 and 200 units
Minimum requirement of B: B >= 40
Maximum requirement of B: B <= 200
Non-negativity Constraint: A, B >= 0
LPP Formulation:
Max Z = 48A + $10B
Subject To:
0.5A + 0.5B <= 150
0.6A + 0.4B <= 145
A >= 30
A <= 150
B >= 40
B <= 200
A, B >= 0
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