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23. Product A offers a profit of Rs 25 per unit and product B yields a profit of Rs 40<br />
per unit. To manufacture the products, leather, wood and glue are required in the<br />
amount as shown below:<br />
Resources required for one unit<br />
Product Leather (kg) Wood (sq m) Glue (litres)<br />
A 0.50 4 0.2<br />
B 0.25 7 0.2<br />
Availability 2200 28000 1400<br />
24.<br />
25.<br />
(a) Formulate the LP model and find the optimal solution.<br />
(b) Which resources are fully consumed? How much of each resource remains<br />
unused?<br />
(c) What are the shadow prices of the resources?<br />
A company manufactures two different kinds of machines, each requiring a<br />
different manufacturing technique. The Deluxe machine requires 18 hours of<br />
labour, 9 hours of testing, and yields a profit of Rs. 400. The Standard machine<br />
requires 3 hours of labour, 4 hours of testing, and yields a profit of Rs. 200.<br />
There are 800 hours of labour and 600 hours of testing available each month. A<br />
marketing forecast has shown that the monthly demand for the Standard<br />
machine to be no more than 250. Management wants to know the number of<br />
each model to produce monthly that will maximise total profits. Formulate and<br />
solve this as a linear programming problem.<br />
A metal product company produces waste cans, filing cabinets, file boxes for<br />
correspondence and lunch boxes. Its inputs are sheet metals of two different<br />
thicknesses, called A and B and manual labour. Input output relationships for<br />
the company are shown in the table.<br />
Waste cans<br />
Filing cabinets Correspondence boxes Lunch<br />
boxes<br />
26.<br />
Sheet metal A 6 0 2 3<br />
Sheet metal B 0 10 0 0<br />
Labour 4 8 2 3<br />
The sales revenue per unit of waste cans, filing cabinets, correspondence boxes<br />
and lunch boxes are Rs 20, Rs 400, Rs 90 and Rs 20, respectively. There are 225<br />
units of Sheet metal A available in the company's inventory, 300 of Sheet metal<br />
B, and 190 units of labour. What is the company's optimal sales revenue?<br />
A knitting machine can produce 1000 trousers or 3000 shirts (or a combination of<br />
the two) each day. The finishing department can handle either 1500 trousers or<br />
2000 shirts (or a combination of the two) each day. The marketing department<br />
requires that at least 400 trousers be produced each day. The company's<br />
objective is profit maximisation. If the profit from the trousers is Rs 40 and that<br />
from a shirt is Rs 15, how many of each type should be produced?
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