Question

4.   A pharmaceutical firm produces different brands of a drug; I, II, III and IV. Each brand contains volume(s) of at least one of chemical X or Y or both. Product I requires a combination of two centimeters square of chemical X and a unit square of chemical Y given a resource constraint of 16. A unit square of chemical X and two centimeters square of chemical Y is needed to produce product II given a resource constraint of 11. Product III needs only chemical X and requires at least two centimeters square volume of chemical X while product IV requires a unit centimeter square of chemical X and three centimeters square of chemical Y with a constraint of 15. The company makes a profit of ¢3000 for using a unit of X and ¢5000 for a unit of Y.
(i)   Write four inequalities involving X and Y that reflect the conditions above
(ii)   Determine, graphically, the best possible combinations of X and Y for the company.
(iii)   Using the objective function, determine the best combination that maximizes the company’s profit.                           25 marks

5.   SBL Ltd decided on the 5th of February to start producing bottled water. By 14th March, SBL Ltd had put all the needed structures at a cost of ¢1000 and indicated a profit before operation to be - ¢1000. They reported that the cost of producing any of their product depends on the function 3Q + 0.004Q2. SBL Ltd further, indicated that additional product produced increases profit by a margin defined by 7 – 0.012Q. Determine;
(i)   The total cost function of SBL Ltd
(ii)   The profit function of SBL Ltd
(iii)   The total revenue function of SBL Ltd (Hint: Profit = TR – TC)
(iv)   The output level that maximizes the firm’s revenue.

detailed answers needed please

Answer 1

using given data and required variables we formulate the problem and find the best combination and maximum profit

as per guidelines only one question is to be solved for remaining qs post separately

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