Linear programming questions | form five Pure Advanced Mathematics

A farmer has two godowns A and B for storing his groundnuts. He stored 80 bags in A and 70 bags in B. Two customers C and D place orders for 35 and 60 bags respectively. The transport costs per bag from each godown to each of the customers are as tabulated below:

How many bags of groundnuts should the farmer deliver to each customer from each godown in order to minimize the total transport cost?

A small furniture company has two workshops which produce timber used in the manufacture of tables and chairs. In one day operation, workshop A can produce timber required to manufacture 20 tables and 60 chairs and workshop B can  produce timber required to manufacture 25 tables and 50 chairs. The company needs enough timber to manufacture at least 200 tables and 500 chairs.

If it costs 100,000/= to operate workshop for one day and 90,000/= to operate workshop B for one day, how many days should each workshop be operated in order to produce a sufficient amount of timber at a minimum cost?. What is the minimum cost?.

A retail shop received orders from two customers A and B for the following food packages : The package for  A should contain 20 kg of beans , 20 kg of rice and 20 kg of maize flour , while that for B should contain 10 kg of beans and 30 kg of rice. The shop has only 340 kg of beans, 540 kg of rice and 280 kg of maize flour. If a unit of package A costs 1,200/= and package B costs 900/= , how many packages should he supply to each of his customers so as to realise the maximum sales?

How much of each commodity does the retailer  above remain with after meeting the order?

Mr. Masumbuko has two traditional stores A and B for storing groundnuts. He stored 80 bags in A and 70 bags in B. Two customers C and D placed orders for 35 and 60 bags respectively. The transport costs per bag from each store are summarized in the following table:

1. How many bags of groundnuts should the farmer deliver to each customer in order to minimize the transportation cost?
2. Determine the minimum cost of transport.

Mama Lishe has 140,80 and 130 units of ingredients A, B and C respectively. A piece of bread requires 1,1 and 2units of A,B, C respectively. A pancake requires 5,2 and 1 units of A, B and C respectively.

1. Taking x and y to be the number of pieces of bread and pancakes respectively, write down three inequalities which satisfy these conditions.
2. Draw a graph which shows a region representing possible values of x and y.
3. If the price for a piece of bread is 300/= and a pancake is 500/=, how many of each snacks should she bake in order to maximize her gross income?
4. What would be her gross income?

Following an illness, a patient is required to take pills containing minerals and vitamins. The contents and costs of two types of pills, Feelgood and Getbetta, together with the patient`s daily requirement, are shown in the following table:

If the daily prescription contains x Feelgood pills and y Getbetta pills, find the cheapest way of prescribing the pills and the cost.

Mr. Safari wants 10, 12 and 12 units of chemicals A,B and C respectively for his garden. A liquid product contains 5 units of A, 2 units of B and 1 unit of C per jar and each jar is sold at 3,000/=. On the other hand a dry product contains 1 unit of A, 2 units of B and 4 units of C per carton and each carton is sold at 2,000/=. If x and y are hte number of jars of liquid products and cartons of dry products respectively, formulate a linear programming problem to minimize the cost.

A cement dealer has two depost; D1 and D2 holding 180 tons and 250tons of cement respectively. The customers C1 and C2 have ordered 200 and 150 tons respectively. The transport cost per ton from each depot to each customer are as shown in the following table:

1. How many tons of cement should be delivered to each customer in order to minimize the transport cost?
2. After the orders, how many tons of cement will remain at D2?