5a. The marginal cost function for a product is given...

5a. The marginal cost function for a product is given by MC(q) = 300 - 1.4q - 6?q, 50?q?120. If the current production level is 90 units and the production is increased to 100 units, find the additional cost if this change is made. (Round to the nearest cent) b. It has been estimated that the marginal cost function for a product is MC(q) = 1800 - 50q - 0.06q^2 ,0?q?150. If the fixed costs are $850, find the total cost of producing 30 units. c. If the marginal revenue obtained from selling the qth unit of a product is given by MR(q) = 5000 - 20q - 0.27q^2 ,0?q?150. what would be the selling price for each unit if 40 units are sold.

Transcript

00:01 Hi, in the given problem we have required to find the additional cost when the unit of production is raised from 90 to 100 and we are given with the marginal cost function so marginal cost function with the function of q which is the quantity is 300 minus 1 .49 minus 6 square root of q now we know that marginal cost of 100 would be equal to 300 so what we'll do it will first find the difference of the marginal cost of hundred and ninety so mc 100 minus mc marginal cost of 90 is what we are required to find so this would be the additional cost that is required so basically we are required to find this additional cost now we know that for mc 100 so this would be or we can say that this can be implied as you using this formula so we can get this as 300 minus 1 .4 times 100 minus 6 times root over 100 then minus of 300 minus 1 .4 into 90 minus 6 root over 90 so after simplifying we get this as minus 17 .08 so this is the required additional call so we can see that the cost will decrease so that the cost will decrease now in the second case we are given with the marginal cost function which is equal to 5 ,000 minus 200 q minus 0 .27 q square so again we are required to find the the total cost or away we will first find the revenue function here so the revenue q would be the integration of this function the marginal marginal revenue function which is marginal revenue function this is 5 ,000 minus 20 q minus 0 .27 q square and integration with respect to dq so that will give us the revenue function so that comes out to be 500 a 5 ,000 q minus 10 q square minus 0 .0 .0 .0 .0 .0 .000 square minus 0 .0 .0.

02:36 0 .09 q.

02:40 Now, so that's the revenue function after finding the integration.

02:45 Now the selling price would be the selling price is the revenue function by the number of quantity sold...

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