- Radioco Manufactures Two Types Of Radios The Only Scarce Resource That Is Needed To Produce Radios Is Labor The Compan 1 (385.88 KiB) Viewed 52 times
- Radioco Manufactures Two Types Of Radios The Only Scarce Resource That Is Needed To Produce Radios Is Labor The Compan 2 (382.67 KiB) Viewed 52 times
Radioco manufactures two types of radios. The only scarce resource that is needed to produce radios is labor. The company now has two laborers. Laborer 1 is willing to work up to 40 hours per week and is paid $5 per hour. Laborer 2 is willing to work up to 50 hours per week and is paid $6 per hour. The price of radio 1 and radio 2 are $25 and $22, respectively. The resources required to build each type of radio are given in Table 1. Table1 Radio 1 Radio 2 Resource Required Resource Required Laborer 1: 1 hour Laborer 1: 2 hours Laborer 2: 2 hours Raw material cost: $5 Laborer 2: 1 hour Raw material cost: $4 In the following questions if you are asked to find the new optimal solution due to a change in one of the parameters start from/use the current optimal tableau! Letting x; be the number of type i radios produced each week. a. (10 pts.) Show that Radioco should solve the following LP (its optimal tableau is given in Table 2, which is given in terms of the equivalent minimization problem). You need to state how the cost coefficients are calculated as they are and why the constraints are as given. maximize 3x] + 2x2 subject to X1 + 2x2 540 2xy + x2 < 50 + X1, X2 > 0
Table 2 X1 X2 X3 X4 80 0 0 1/3 4/3 X] = 20 1 0 -1/3 2/3 X2 = 10 0 1 2/3 -1/3 b. (10 pts.) For what values of the price of a Type 1 radio, would the current solution of producing 20 type 1 radios and 10 type 2 radios remain optimal? c. (10 pts.) If the price of of type 1 radio becomes $22 what is the new optimal solution ? d. (10 pts.) For what values of the price of a Type 2 radio, would the current solution of producing 20 type 1 radios and 10 type 2 radios remain optimal? e. (10 pts.) If laborer 2 were willing to work as many as 60 hours per week, would the current basis remain optimal? What would be the new optimal solution? f. (10 pts.) If laborer 2 were willing to work as many as 90 hours per week, would the current basis remain optimal? What would be the new optimal solution? g. (10 pts.) If laborer I were willing to work an additional hour, what is the most that Radioco should pay? h. (10 pts.) A Type 3 radio is under consideration for production. The specifications of a Type 3 radio are as follows: price, $30: 2 hours from laborer 1: 2 hours from laborer 2; cost of raw materials, $3. Should Radioco manufacture any Type 3 radios and if so how many? i. (10 pts.) Suppose, in addition to the existing constraints, that each radio l needs 5 transistors while each radio 2 needs 4 transistors in the production. However, the suppliers can only supply 120 transistors per week. What is the new optimal solution? How many radios of each type should be produced?