--%>

Problem on Decision variables

A factory has three distinct systems for making similar product:

System 1: Worker runs 3 machines of type-A, each of which costs $20 per day to run, each generates 100 units per day and the worker is paid $40 per day.
System 2: Worker runs 5 machines of type-A, each of which costs $20 per day to run, generates 70 units per day and the worker is paid $50 per day.
System 3: Worker runs 2 machines of type-B, each of which costs $35 per day to run, generates 160 units per day and the worker is paid $60 per day.
There are 45 machines of type-A, 10 of type-B and 16 workers. Each and every unit can be sold for $50.

Give answers to the questions below:

1. Give a model which explains how production must be organized so as to maximize gain. Clearly explain all computations, formulas and model.

2. Give an optimal solution to your model supposing continuous decision variables (explain the solution).

3. Determine the maximum amount you would pay for an extra machine type A, B? How did you come up to this conclusion? Would you hire additional workers? Determine the maximum you would pay per day?

E

Expert

Verified

(1) Decision variables:

X1 - Number of setups as system 1
X2 – Number of setups as system 2
X3 – Number of setups as system 3

Objective function
Max Z = $15000X1 + $17500X2 + $16000X3 - $40X1 - $60X1 - $50X2 - $100X2 - $60X3 - $70X3
Max Z = $14900X1 + $17350X2 + $15870X3
For X1, the revenue = 3machines*100units*selling price$50 = $15,000 and similarly for others.

Constraints
3X1 + 5X2 ≤ 45 (constraint for type A machines)
2X3 ≤ 10 (constraint for type B machines)
X1 + X2 + X3 ≤ 16 (constraint for workers)
X1, X2, X3 ≥ 0 (continuous decision variable and so integer is not assumed)

(2) The optimal solution was found using excel solver and it was found to be 5 setups of system 1, 6 setups of system 2 and 5 setups of system 3 to achieve a maximum profit of $257,950.

(3) The maximum amount that could be paid for an extra machine for type A is $1225 and that for type B is $2322.5, since increase in these availability values by 1 unit will increase the total profit by $1225 and $2322.5 respectively (meaning they are Lagrange multipliers for type A and B machines). Yes, it is profitable to hire extra workers. An increase in the number of workers by 1 per day can increase the profit by $11225 (Lagrange multiplier for worker usage). Hence the maximum that could be paid per day is $11225.

   Related Questions in Corporate Finance

  • Q : Explain definition of put–call parity

    Explain the definition of put–call parity described by Reinach.

  • Q : Zero coupon bonds problem Shana wants

    Shana wants to purchase 5-year zero coupon bonds with a face value of $1,000. Her opportunity cost is 8.5 %. Supposing annual compounding, what would be the present market price of such bonds? (Round to the closest dollar.) (a) $1,023  (b) $665  (c) $890&nbs

  • Q : Explain Value Chain Value Chain : The

    Value Chain: The value chain is a theory from business management that was first described and popularized Michel Porter in his 1985 best seller, Competitive Advantage: Creating and Sustaining Superior Performance.

  • Q : Explain the Monte Carlo evaluation of

    Explain the Monte Carlo evaluation of integrals.

  • Q : What is the expected risk premium on

    You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z. Theprobability of the state of the economy is Boom 25%; Normal 60%; and, Bust 15%. The rateof return for stock X is Boom .20; Normal .15; and, Bust .00. The rate of return for stock Y is

  • Q : Define Effective Utilization of Funds

    Effective Utilization of Funds: It is just the decision to maximize the return on investment of funds. When finance manager is not capable to raise the return by investing fund in profitable assets or other profitable projects, company’s busines

  • Q : Define Economy Impacts Economy Impacts

    Economy Impacts: An upcoming economy is indicated by rise in stock market, as stock market is primary indicator of a economic strength of a country. Progressing economy results in market boom. Yield of companies’ increases on improving economy,

  • Q : Active versus Passive fund managers

    Active vs. Passive fund managers: Passive fund managers adopt a long term buy and hold strategy. Usually, stocks are purchased so that the portfolio’s returns will track those of an

  • Q : Who were the creators of uncertain

    Who were the creators of uncertain volatility model?

  • Q : What is the impact of auto portfolio

    What is the impact of auto portfolio into the quotation of the shares?