Quantitative Techniques

Q1. Find elasticity of demand of the function x=150-5P at (1) P=15, (2) P=20.

Q2. Find dy/dx of the following cases 1. y=x2 log x. 2. log x /x.

Q3. A revenue function is given by R= 35x-2x2 where R is the revenue and x is the quantity. What value of x maximizes revenue? What is the Maximum Revenue?

Q4. If a person deposits on a recurring deposit scheme, monthly Rs. 1500 for 4 years at 15% per annum, what would be the sum that can be received at the end of 4 years.

OPERATION MGMT

Q5. Serra's Ceramics spent 3 000 MU on a new kiln last year, in the belief that it would cut energy usage 25 % over the old kiln. This kiln is an oven that turns "green ware" into finished pottery. Serra is concerned that the new kiln requires extra labor hours for its operation. Serra wants to check the energy saving of the new oven, and also to look over other measures of their productivity to see if the change really was beneficial. Serra has the following data to work with: Last Year This Year Production (finished units) 4000 4000 Green ware (pounds) 5000 5000 Labor (hrs) 350 375 Capital (MU) 15000 18000 Energy (kWh) 3000 2600 Were the modifications BENEFICIAL?

Q6. The Cool-Tech Co. produces various types of fans. In May, the company produced 1728 window fans at a standard price of 40 MU. The Co. has 12 direct labour employees whose compensation (including wages and fringe benefits) amounts to 21 MU/hour. During May, window fans were produced on 9 working days 9of 8 hours each), and other products were produced on other days. a. Determine the productivity of the window fans. b. In June, the CoolTech Co. produced 1 730 fans in 10 working days. What is the percentage in labor productivity of windows from May?

Q7. Mr. Ilhan DALCI makes billiard balls in his Beyarmudu plant. With a recent increase in taxes, his costs have gone up and he has a newfound interest in efficiency. Mr.Dalci is interested in determining the productivity of his organization. He would like to know if his organization is maintaining the manufacturing average of 3% increase in productivity. He has the following data representing a month from last year and an equivalent month this year. __________________Last year Now Units produced 1 000 1 000 Labor (hours) 300 275 Resin (kg.s) 50 45 Capital invested (MU) 10 000 11 000 Energy (BTU) 3 000 2 850 Show the productivity change for each category and then determine the IMPROVEMENT for labor- hrs, the typical standard for comparison.