Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contri
bution per tire are given in the following table. Manufacturing Time Hours) Time Available Operation aterial Preparation Tire Building Curing Final Inspection rofit Tire Economy tiresPremium tires Hours 600 650 580 120 4/3 1/2 1/2 1/5 $12 2/4 1/3 $10 Answer the following assuming that the company is interested in maximizing the total profit contribution.
a. What is the linear programming model for this probiem?
b. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?
a. What is the linear programming model for this probiem?
b. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?
1 answer:
Answer:
(a)Let X1 be the number of economy tires and X2 be the number of premium tires.
Objective function:
Maximize Z, where Z = 12X1 + 10X2
Subject to constraints
4X1/3 + X2/2 <= 600
4X1/5 + X2 <= 650
X1/2 + 2X/4 <= 580
X1/5 + X2/3 <= 120
X1, X2 = Z
(b) Check attachment for spreadsheet
(c) The maximum profit that can be obtained is $6032
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Answer:
attached is the diagram
Explanation:
Each extra worker produces an extra unit of output, is said to be the marginal production of an extra worker employed
marginal production :
change in total production / change in labor = ΔTp / ΔL
Average production = Tp / L
Tp = total production , L = number of labor
To draw the Total product of labor , average product labor and marginal product labor curves starting from zero labor
0 worker : Total product = 0, average product labor = 0 , marginal = 0
1 worker : Total product = 1, average product = 1 , marginal = 0
2 worker : Total product = 2, average product = 1, marginal = 1
3 workers: total product = 3 average product = 1, marginal = 1
4 workers: Total product = 4, average product = 1, marginal = 1
5 workers : Total product = 5 average product = 1, marginal = 1
6 workers : total product = 6 average product = 1 , marginal = 1
7 workers : total product = 7 , average product = 0.85, marginal = 0
8 workers : total product = 8, average product = 0.75 marginal = 0
